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WorksheetsSU5K9Z AP Calc Final Review S1
Total questions: 192
Worksheet time: 10hrs 40mins
Name
Class
Date
1.
The second derivative of the function f is given by f''(x)= x(x-a)(x-b)^2. The graph of f'' is shown. For what values of x does the graph of f have an inflection point?
a)
0 and b only
b)
0 and a only
c)
j and k only
d)
SU0, a, and b
2.
A particle moves along the x-axis so that at time t ≥ 0 its velocity is given by v(t)= 3 + 4.1 cos(0.9t). What is the acceleration of the particle at time t= 4?
a)
-2.016
b)
-0.677
c)
1.633
d)
1.814
3.
For the function f(x)= x3 - 4x2- 4x +16: Find the point(s) of inflection of the function.
a)
1
b)
4/3
c)
3/4
d)
1/2
4.
A snail moves along the x-axis so that her position is modeled by the equation f(t)= t3- 12t2+ 36t. Find her acceleration at time t and after 3 second.
a)
7t-55, a(3)= -6
b)
3t-24, a(3)= 10
c)
6t-24, a(3)= -6
d)
6t-24, a(3)= 6
5.
A snail moves along the x-axis so that her position is modeled by the equation f(t)= t3- 12t2+ 36t. When is she slowing down?
a)
(2,4)
b)
(0,2) u (4,6)
c)
(0,4)
d)
(4,6) u (8,10)
6.
When is the graph of f(x)= x3-x2 concave down?
a)
(-∞, 1/3)
b)
(1/3, ∞)
c)
(2, ∞)
d)
(-∞, 6)
7.
A local minimum value of the function y= ex/x is:
a)
1/e
b)
1
c)
-1
d)
e
8.
Let f'(x)= esinx - 2cosx. How many points of inflection does the graph of f have on the interval [0,4]?
a)
none
b)
1
c)
2
d)
3
9.
Which of the following are the absolute extrema of f(x)= 3x2- 9x+ 8 on the interval [-2,2]?
a)
max 8, min 5/4
b)
min 5/4
c)
max 38, min 5/4
d)
max 2, min 5/4
10.
A particle moves along the x-axis so that at time t ≥ 0 its position is given by s(t)= 2t3- 21t2+ 72t- 53. At what time is the particle at rest?
a)
t=3 only
b)
t=4 only
c)
t=3 and t=7/2
d)
t=3 and t=4
11.
a)
2
b)
15/4
c)
18/5
d)
26/7
12.
Evaluate f(x)=3-½x from 2≤x≤14
a)
8
b)
13
c)
-12
d)
-⅝
13.
Evaluate f(x)=sinx from 0≤x≤3π⁄2
a)
1
b)
7
c)
2π
d)
9/2
14.
Evaluate f(x)=x²-2x from 0≤x≤3
a)
0
b)
15
c)
¾
d)
9
15.
a)
3.896
b)
6
c)
9.345
d)
2.389
16.
a)
15.9
b)
178.475
c)
124.616
d)
19.25
17.
a)
1.590
b)
5.079
c)
0.583
d)
2.689
18.
a)
67
b)
12
c)
19
d)
21
19.
a)
2
b)
6
c)
1
d)
0
20.
a)
474
b)
414
c)
312
d)
342
21.
True or false: we find rates of change by calculating the slope of a secant line?
a)
True
b)
False
22.
True or false: instantaneous rate of change is found using f'(x)
a)
True
b)
False
23.
What number does the limit of Δx approach when finding instantaneous R.O.C.?
a)
∞
b)
-∞
c)
0
24.
Find the average rate of change for the following points: (6,9) and (4,20)
a)
4
b)
32
c)
-11/2
d)
-2/11
25.
Find the average ROC for the following function at the points (1,4) and (0,1): 3X+1
a)
12
b)
3
c)
4
d)
23
26.
Find the average rate of change for the following points: (6,7) and (4,5)
a)
-1
b)
1
c)
2
d)
0
27.
Find the average rate of change for the following points: (-9,0) and (3,-6)
a)
-2
b)
2
c)
-1/2
d)
1/2
28.
Find the instantaneous ROC for the following function @ x=2: 2X2 +X
a)
9
b)
3
c)
4
d)
7
29.
Find the instantaneous ROC for the following function @x=1: X3
a)
2
b)
3
c)
7
d)
10
30.
Find the instantaneous ROC for the following function @x=2: X2+4X+4
a)
4
b)
15
c)
3
d)
6
31.
Evaluate
a)
(1/2x^8)-x^2+15lnx+c
b)
<--
32.
Evaluate
a)
(1/9x^9)-(1/7x^-7)+c
b)
<--
33.
Evaluate
a)
(5/4t^4)+(2t^-5)+4t+c
b)
<--
34.
Evaluate
a)
(1/3x^3)-4sqrtx+c
b)
<--
35.
Evaluate
a)
sinx+(1/4x^2)+c
b)
<--
36.
Evaluate
a)
tanx+c
b)
<--
37.
Evaluate
a)
2t+(1/3t^3)-t^2-(1/4t^4)+c
b)
<--
38.
Evaluate
a)
(1/3x^3)-1/x+c
b)
<--
39.
Evaluate
a)
(2x^5)-2tanx+c
b)
<--
40.
Evaluate
a)
(5/4x^4)+2sinx+c
b)
<--
41.
Solve for y': X3+y3=6xy
a)
y'=(3y-6x2)/(6y2-3x)
b)
y'=(6y-3x2)/(3y2-6x)
42.
Solve for y': x2y2+x(siny)=4
a)
y'=(-2xy2-siny)/(2x2y+x(cosy))
b)
y'=(2x2y+cosy)/(2xy2+y(cosx))
43.
Solve for y': (xy)1/2=1+sin(xy)
a)
y'=(eysinx+ycos(xy))/(eycosx-xcos(xy))
b)
y'=(eysiny+ycos(y))/(eysinx-ycos(x))
44.
Calculate the derivative: 2y3+6x2y-12x2+6y=1
a)
y'=(4x+6xy)/(y2+x2+1)
b)
y'=(4x-2xy)/(x2+y2+1)
45.
Solve for y': x4(x+y)=y2(3x-y)
a)
y'=(3y2-5x4-4x3y)/(x4+3y2-6xy)
b)
y'=(3y2+5x4-4x3)/(x4+3y2-4y)
46.
Find the derivative of the function: y=sin-1(2x+1)
a)
y'=1/[(2x2-2x)1/2]
b)
y'=1/[(-x2-x)1/2]
47.
If a function is continuous at each point on a closed interval [a,b] and is differentiable on (a,b) then there is at lest one number c on (a,b) such that f(b)-f(a)/b-a =f1(c)
a)
R-Ram
b)
Concave up
c)
Mean Value Theorem
d)
Slope of the tangent line
48.
Find the value of c guaranteed by the MVT for f(x)= lnx on [1, e^2]
a)
E^2-1
________
2
________
2
b)
1
_____
X
_____
X
c)
1
d)
0
49.
How many values of c satisfy the conclusion of the MVT for f(x)=x^3+1 on [-1, 1]?
a)
3
b)
1
c)
0
d)
2
50.
The function f(x)=x^3-4x^2+3x is defined for all x on the closed interval [0,4]. For what value of (0,4) is the slope of the tangent line to the graph of f equal to the slope of the secant line connecting (0, f(0)) and (4, f(4))
a)
7
b)
3/2
c)
8/3
d)
4
51.
Find the number c that satisfies the conclusion of the MVT for f on the closed interval [1,3]
a)
(13/3)^1/2
b)
6
c)
(18/3)^1/2
d)
2
52.
f(x)=x^2-6x+8, [2,5] find c (2,5)
a)
3/2
b)
7/2
c)
4
d)
2
53.
Let f(x) = x^3+9x^2+13 and let c be the number that satisfies the MVT for f on the interval
-7 is less than or equal to x which is less than or equal to -1
-7 is less than or equal to x which is less than or equal to -1
a)
-6
b)
-3
c)
-5
d)
-2
54.
Let f(x)= x^3-6x^2+12x and let c be the number that satisfies the MVT for f on the interval [0,3]
a)
2
b)
0
c)
3
d)
1
55.
Let g(x)= x^3+12x^2+36x and let c be the number that satisfies g on the interval
-8 is less than or equal to x which is less than or equal to -2
-8 is less than or equal to x which is less than or equal to -2
a)
-6
b)
-1
c)
-3
d)
-7
56.
Let g(x)= x^3-16x and let c be the number that satisfies the MVT for g on the interval [-4,2]
a)
0
b)
1
c)
-3
d)
-2
57.
a)
1/3
b)
-3/2
c)
7/5
d)
3/2
58.
a)
0
b)
2/3
c)
1
d)
1/3
59.
a)
K/P
b)
K/2
c)
2/pk
d)
K/2p
60.
a)
(Sqrt2)/5
b)
(Sqrt2)/3
c)
2/3
d)
2/5
61.
a)
3
b)
1
c)
DNE
d)
Sqrt3
62.
a)
-1/4
b)
1/2
c)
1/4
d)
1
63.
a)
8
b)
Sqrt8
c)
8/2
d)
(Sqrt8)/2
64.
a)
Infinit
b)
0
c)
1
d)
- infinity
65.
a)
-3/2
b)
4/5
c)
1/2
d)
3/2
66.
a)
1
b)
- infinity
c)
-1
d)
Infinity
67.
A spherical balloon is being filled with helium at the rate of 4ft^3/min. Find the rate, in ft/min, at which the surface area is increasing when the volume is (32pi/3) cubic feet:
Note: for a sphere, V= (4pi r^3/3), SA= 4pi r^2
Note: for a sphere, V= (4pi r^3/3), SA= 4pi r^2
a)
4pi
b)
2
c)
4
d)
2pi
68.
The radius of a circle is increasing at a constant rate of 0.2 meters per second. What is the rate of increase in the area of the circle at the instant when the circumference of the circle is 20pi meters?
a)
0.4pi m^2/sec
b)
4pi m^2/sec
c)
20pi m^2/sec
d)
100pi m^2/sec
69.
If a snowball melts so that its surface area decreases at a rate of 1 cm^2/min, find the rate at which the diameter decreases when the diameter is 10 cm.
a)
-1/20pi cm/min
b)
20pi cm/min
c)
2pi cm/min
70.
Gravel is being dumped from a conveyor belt at a rate of 30 ft^3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10ft high?
a)
5/6pi ft/min
b)
6/5pi ft/min
c)
5pi ft/min
d)
6pi ft/min
71.
A ladder 10ft long rests against a vertical wall. If the bottom slides away from the wall at a rate of 2ft/sec, how fast is the angle between the top of the ladder and the wall changing when the angle is pi/4 radians?
a)
sqrt 5/2 rad/sec
b)
sqrt 2/5 rad/sec
c)
2/5 rad/sec
d)
5 rad/sec
72.
A ship is 400 miles south of Tahiti and is sailing south at 20 miles/hour. Another ship is 300 miles eat of Tahiti and is sailing west at 15 miles/hour. At what rate is the distance between the ships changing?
a)
8 mi/h
b)
6 mi/h
c)
7 mi/h
d)
9 mi/h
73.
The quantities P, Q, and R are functions of time, t, and are related by the equation R= PQ. Assume that P is increasing instantaneously at the rate of 8% per year and that Q is decreasing instantaneously at the rate of 2% per year. Determine the percentage rate of change for R.
a)
.06
b)
.0006
c)
.09
d)
.60
74.
A 20 meter ladder rests vertically against the side of a barn. A pig that has been hitched to the ladder starts to pull the base of the ladder away from the wall at a constant rate of 40 cm per second. Find the rate of change of the height of the top of the ladder after 30 seconds.
a)
3 m/s
b)
5 m/s
c)
-0.3 m/s
d)
0.6 m/s
75.
A screensaver displays the outline of a 3cm x 2cm rectangle and then expands the rectangle in such a way that the 2cm side is expanding at the rate of 4 cm/sec and the proportions of the rectangle never change. How fast is the area of the rectangle increasing when its dimensions are 12 cm x 8 cm?
a)
87 cm^2/sec
b)
30 cm^2/sec
c)
20 cm^2/sec
d)
96 cm^2/sec
76.
A spherical snowball melts so that its surface area shrinks at the constant rate of 10 square centimeters per minute. What is the rate of change of volume when the snowball is 12 centimeters in diameter.
a)
-50 cm^3/min
b)
-30 cm^3/min
c)
20 cm^3/min
d)
30 cm^3/min
77.
The second derivative of the function is given by f"(x)=x(x-a)(x-b)^2. The graph of f" is shown. For what values of x does the graph of f have an inflection point?
a)
0 and a only
b)
0 and m only
c)
b and j only
d)
0, a, and b
78.
The derivative of a function g is continuous and has exactly two zeros. Selected values of g' are given in the table above. If the domain of g is the set of all real numbers, then g is decreasing on which of the following intervals?
a)
-2<x<2 only
b)
-1<x<1 only
c)
x>2 only
d)
x>-2
79.
The function f has first derivative (look at image). What is the x-coordinate of the inflection point of the graph of f?
a)
1.008
b)
0.473
c)
0
d)
-0.278
80.
The graph of f'(x) is shown. For which inputs, x, is the graph increasing?
a)
(3, infinity)
b)
(0,3)
c)
(-infinity, 3)
81.
Using the shame graph of f'(x) as the problem before. For which inputs, x, is the graph of f decreasing?
a)
(3, infinity)
b)
(0,3)
c)
(-infinity, 3)
82.
Approximately how much less than 4 is (63)^(1/3)?
a)
1/48
b)
1/16
c)
1/3
d)
2/3
83.
The best linear approximation for f(x) = tan x near x = 𝜋/4 is
a)
1 + (1/2) (𝑥 − 𝜋/4 )
b)
1 + (𝑥 − 𝜋/4 )
c)
1 + 2(𝑥 − 𝜋/4 )
d)
2 + 2(𝑥 − 𝜋/4 )
84.
When h is near zero, e^(kh), using local linearization, is approximately
a)
kh
b)
1
c)
1+k
d)
1+kh
85.
if f(x)=(1-x)^(1/2) and a=0 approximate (0.9)^(1/2)
a)
1.5
b)
0.95
c)
2
86.
if g(x)=(1+x)^(1/3) at a=o approximate (0.95)^(1/3)
a)
2.674
b)
3.78
c)
.983
87.
Find f if f '' (x) = 2-12x , f(0) = 9, and f(2)= 15
a)
F(x) = x2 - 2x3 +9x - 15
b)
F(x) = x2 - 2x3 +9x - 30
c)
F(x) = x2 - 2x3 +9x- 9
88.
The most general antiderivative of f(x) = 8x9 - 3x6 + 12x3
a)
F(x) = 72x8 - 185 + 36x2
b)
F(x)= 4/5x10 - 3/7x7 + 3x4
c)
F(x)= 8/10x10 - 3/7x7 + 12/4x4
89.
Find the antiderivative of f(x) = 5x4 - 2x5 that satisfies the given condition F(0)= 4
a)
x5 -1/3x6 + 4
b)
5x4 -1/3x6 + 4
c)
x5 -1/3x6 + 2
d)
5x4 -1/3x6 + 2
90.
Antiderivative of 1/x
a)
ex
b)
ln(x)
c)
x-1
d)
x
91.
Find f from f '' (x) = 2 +cos x , f(0)= -1 , and f (pi/2) = 0.
What number does the letter c stand for?
What number does the letter c stand for?
a)
c=pi/4
b)
c=pi/2
c)
c=pi
d)
c=0
92.
if f '(x) = 20/(1+ 2x), Find F(x)
a)
20 tan x + c
b)
20arctan-1x + c
c)
20arctan-1x
d)
20 tan x
93.
f(x) = sinx + 30
find F(x)
find F(x)
a)
cos x + c
b)
cos x + 30x
c)
sinx + 30x
d)
- cos x + 30x
94.
A particle moves on a straight line and has an acceleration given by a(t) = 6t +4 . Its initial velocity is v(0)= -6 and its initial displacement is s(0) = 9. Find the position function s(t)
a)
t3 + 2t2 - 6t + 9
b)
t3 + 2t2 - 6t -9
c)
t3 + 2t2 - 9
95.
Given f(x) = 3x2 - 2x +3, find the average value of f on [1,2]
a)
13
b)
6.5
c)
7
d)
3.5
96.
f(x) = (x5 - x3 + 2x) / x4
Find F(x)
Find F(x)
a)
F(x) = 1/2x2 - ln(x) - x-2 + c
b)
F(x) = 1/2x2 - ln(x) - x-1 + c
c)
F(x) = 1/2x2 - ln(x) - x-2
d)
F(x) = 1/2x2 - ln(x) - x-1
97.
y=ln(tan x). Find y'
a)
2/(sin 2x)
b)
1/(x tan x)
c)
cot x
d)
sec2x/(tan x)
98.
d/dx(sec x)=
a)
sec x tan x
b)
tan x
c)
sec2x
d)
cot x
99.
y=sin x2. find y'
a)
2 cos x2
b)
2x cos x2
c)
-2x cos x2
d)
cos x2
100.
y=(1+sin x)/(x+cos x)
a)
cos x/ (x+cos x)
b)
(x cos x)/(x+cos x)2
c)
(x+cos x)2
d)
x cos x
101.
y=(3x)2. Find y'
a)
9x
b)
2x
c)
6x
d)
18x
102.
y=(2x+6)12. Find y'
a)
24(2x+6)11
b)
12(2x+6)
c)
12(2x+6)11
d)
-24(2x+6)11
103.
d/dx(cot x)=
a)
cos x
b)
tan x
c)
-csc2x
d)
sec x tan x
104.
y=(x3+x)5. Find y'
a)
3x2+1
b)
5(x3+x)4
c)
(15x2+5)(x3+x)4
d)
5(3x2+1)
105.
y=tan(x2)
a)
sec2(x2)
b)
2x sec2(x2)
c)
2x sec(x2)
d)
sec(x2)
106.
y=exsin x. Find y'
a)
ex(sin x + cos x)
b)
excos x
c)
ex+cos x
d)
ln(sin x)
107.
We use LHOP if the limit is equal to what?
a)
1/0
b)
0/0
c)
infinity/1
d)
1/1
108.
limx→∞ x sin (1/x)
a)
0
b)
-1
c)
does not exist
d)
1
109.
limx→∞ xe-x
a)
0
b)
1
c)
-1
d)
0.5
110.
limx→1 5lnx/ x-1
a)
1/5
b)
5
c)
1
d)
15
111.
limx→0 3x/ln (x+1)
a)
0
b)
1/3
c)
3
d)
infinity
112.
limx→0+ 5x2 lnx
a)
2
b)
-1
c)
5
d)
0
113.
limx→∞(4x) e-x
a)
0
b)
4
c)
1
d)
1/4
114.
limx→∞ (4x2-5x)/(1-3x2)
a)
3/4
b)
-3/4
c)
4/3
d)
-4/3
115.
limx→π/2 (3sec x - 3tan x)
a)
π
b)
3
c)
0
d)
DNE
116.
Estimate the area under the graph of f(x)= x^1/2 from x= 0 to x= 4 using four approximating rectangles and right endpoints. Tell if it is an overestimate or underestimate.
a)
6.416 underestimate
b)
4.146 underestimate
c)
6.416 overestimate
d)
4.146 overestimate
117.
Estimate the area under the graph of f(x)= cosx from x= 0 to x= pi/2 using four approximating rectangles and left endpoints. Tell if it is an overestimate or underestimate.
a)
.719 underestimate
b)
1.183 underestimate
c)
.719 overestimate
d)
1.183 overestimate
118.
Estimate the area under the graph of f(x)= 2x2 from x= 0 to x= 4 using four approximating rectangles and left endpoints. Tell if it is an overestimate or underestimate.
a)
28 underestimation
b)
60 underestimation
c)
28 overestimation
d)
60 overestimation
119.
Approximate the area under the curve y= squareroot(x) from x=0 to x= 6 using 6 trapezoids.
a)
9.091 u2
b)
12.036 u2
120.
What does RAM measure?
a)
volume under the curve
b)
space under the curve
c)
area under the curve
d)
length under the curve
121.
The more rectangles you have......
a)
the harder it is the solve
b)
the approximation is better
c)
the approximation is poor
d)
the bigger the difference is between left and right
122.
Approximate the area under the curve y= x2+3 from x=0 to x= 3 using M-RAM.
a)
71/4 u2
b)
71/8 u2
c)
68/4 u2
d)
68/8 u2
124.
Approximate the area under the curve y= x2 from x= 0 to x=3 using 6 rectangles and right endpoints.
a)
11.345 u2
b)
11.267 u2
c)
11.875 u2
d)
11.375 u2
124.
Approximate the area under the curve y= x2 from x= 0 to x=3 using 6 rectangles and right endpoints.
a)
11.345 u2
b)
11.267 u2
c)
11.875 u2
d)
11.375 u2
125.
Approximate the area under the curve y= x2 from x= 0 to x= 3 using 6 trapezoids.
a)
18.250 u2
b)
14.653 u2
c)
9.125 u2
d)
7.344 u2
126.
Estimate the area under the curve f(x)= 1 + x2 from x=-1 to x= 2 using six approximating rectangles and left endpoints.
a)
5.375 u2
b)
6.872 u2
c)
8 u2
d)
5u2
127.
Which of the following are true?
a)
I only
b)
II only
c)
I and II
d)
All of them
128.
for what value of k, is f continuous at x=2
a)
1
b)
2
c)
3
d)
7
129.
Which of the statements are true?
a)
I only
b)
II only
c)
I and II
d)
None of them
130.
Then, f is continuous:
a)
Except at x=1
b)
Except at x=2
c)
Except at x=1 or 2
d)
At each real number
131.
Which of the following statements is true about the graph of f(x)?
a)
Both lim x→6⁻ f(x) and lim x→6⁺
b)
lim x→6 f(x) exists
c)
g is continuous at x=6
d)
None of the above
132.
Find the constant(s) that make the function continuous on (-∞,∞).
a)
-4, 2
b)
2, 4
c)
2
d)
-2, 4
133.
Find the values of c and d that make the function continuous on (-∞,∞)
a)
c=2, d=0
b)
c=8, d=2
c)
c=1, d=2
d)
c=2, d=8
134.
Which of the following is true about f?
a)
I only
b)
I and II
c)
III only
d)
All of them
135.
If 𝑓(𝑥) = x³−x²+x, using the Intermediate Value Theorem, is there a number c such that 𝑓(𝑐) = 10 on the interval [−1,4]?
a)
Yes
b)
No
136.
Which of the following statements is true about the graph of h(x)?
a)
Both lim x→-1⁻ h(x) and lim x→-1⁺ h(x) exist
b)
lim x→-1 h(x) exists
c)
h(x) is continuous at x=-1
d)
None of the above
137.
lim (2/|x|)
x →0+
x →0+
a)
∞
b)
0
c)
-1
d)
1
138.
lim((4-2x/|4-2x|)
x→2+
x→2+
a)
0
b)
∞
c)
-1
d)
1
139.
lim((|2-x|/(x2-4))
x→2+
x→2+
a)
-2
b)
1/4
c)
1/2
d)
∞
140.
lim(|x|/x)
x→0+
x→0+
a)
0
b)
1
c)
-1
d)
∞
141.
lim((|x-5|)/(x-5))
x→5-
x→5-
a)
-1
b)
1
c)
-4
d)
∞
142.
lim((|x-5|)/(x-5))
x→5+
x→5+
a)
-1
b)
1
c)
-4
d)
∞
143.
lim(|x-3|)
x→3
x→3
a)
0
b)
1
c)
-1
d)
∞
144.
lim((|x+1|)/(x+1))
x→-1
x→-1
a)
DNE
b)
-1
c)
1
d)
-∞
145.
lim((16-x2)/(|x-4|)
x→4+
x→4+
a)
4
b)
-8
c)
8
d)
DNE
146.
True or False: FTC states that f must be continuous on [a,b]
a)
True
b)
False
147.
True or False: FTC requires that F be an antiderivative of f over THE ENTIRE interval
a)
True
b)
False
148.
If f is continuous on [a,b] and F is any antiderivative of f on [a,b], then..
a)
F(a)-F(b)
b)
F(x)
c)
F(b)-F(a)
d)
F(b)=F(a)
149.
Find f(4)
a)
41.235
b)
39.036
c)
39.991
d)
17.736
150.
Evaluate
a)
128/3
b)
8/3
c)
11/12
d)
9/10
151.
The derivative of an integral with respect to its upper limit is equal to...
a)
The upper limit of integration
b)
The derivative of the upper limit
c)
The integrand evaluated at the upper limit
d)
The integrand evaluated at the upper limit times the derivative of the upper limit
152.
Find d/dx
a)
sinx
b)
cosx
c)
sec^2x
d)
cost
153.
find g'(x)
a)
-x^2
b)
x^2
c)
u^2
d)
2x
154.
Find d/dx g(x)
a)
sec^2(x^4)
b)
tan(x^4)
c)
4x^3sec^2(x^4)
d)
4xsec^2
155.
Find g'(x)
a)
sqrt(1+x^6)
b)
1+x^6
c)
sqrt(1+r^3)
d)
2xsqrt(1+x^6)
156.
A man is going to use 600yd of fencing to enclose and subdivide a rectangular field into 2 plots with a fence parallel to one side. Of all possible fields that can be fenced, what are the dimensions of the one with the maximum area?
a)
100yd x 150yd
b)
125d x 200yd
c)
90yd X 160yd
157.
A closed rectangular container with a square base is to be made from two different materials. The material for the base costs $5 per square foot and the material for the other 5 sides cost $1 per square foot. Find the dimensions of the container which has the largest volume if the total cost of materials is $72.
a)
4 X 3 X 3
b)
2 X 2 X 6
c)
2 X 4 X 4
158.
A container in the shape of a right circular cylinder with no top has a surface area of 3(pi) ft^2. What height (h) and base radius (r) will maximize the volume of the cylinder?
a)
1 X 1
b)
6 X 4
c)
2 X 1
d)
3 X 5
159.
An open box is made by cutting out squares from the corners of a rectangular piece of cardboard and then turning the sides up. Find the dimensions of the box with the largest volume if the piece of cardboard is 12 inches by 24 inches.
a)
12+4(sqrt3) X 4(sqrt3) X 6-2(sqrt3)
b)
4 X 8 X 1
c)
8(sqrt3) X 16-2(sqrt3) X 8-4(sqrt3)
d)
8 X 5 X 7
160.
Solve
a)
8 x 28 x 19
b)
10 X 30 X 15
c)
5 X 20 X 40
161.
Solve
a)
X=3 y=6
b)
X=6 y=3
c)
X=5 y=4
d)
X=4 y=5
162.
solve
a)
(Sqrt1/2, 1/2)
b)
(7/2, sqrt7/2)
c)
(2, 7)
d)
(7, 2)
163.
If y = 5ex + 6x2 - eπ, find y'.
a)
y' = 5 + 12x - eπ
b)
y' = 5ex + 12x
c)
y' = 5ex + 12x - eπ
164.
Find the equation of the tangent line to y = x√x at the point (4, 8)
a)
y = 3x - 4
b)
y = -1/3x - 4
165.
Differentiate the function: f(x) = 186.5
a)
f'(x) = 186.5x
b)
f'(x) = 0
166.
Differentiate the function: f(x) = 1/4 (t4 +8)
a)
f'(x) = t3
b)
f'(x) = 4t3
167.
Differentiate the function: y = 5ex + 3
a)
y' = 5ex
b)
y' = ex + 3
168.
Find f'(x). f(x) = 3x5 - 20x3 + 50x
a)
f'(x) = 60x3 - 120x2
b)
f'(x) = 15x4 - 60x2 + 50
169.
Find f'(x). f(x) = x + 1/x
a)
f'(x) = x + x-1
b)
f'(x) = 1- x-2
170.
Find an equation of the tangent line to the curve at the given point.
y = 3x2 - x3 , (1,2)
y = 3x2 - x3 , (1,2)
a)
y = 3x-1
b)
y = -1/3x -1
c)
y = 3x2 - 1
171.
Find the first and second derivatives of the function.
f(x) = x4 - 3x3 +16x
f(x) = x4 - 3x3 +16x
a)
f'(x) = 4x3 - 9x2 + 16
f''(x) = 12x2 - 18x
f''(x) = 12x2 - 18x
b)
f'(x) = 4x3 - 6x2 + 16
f''(x) = 7x2 - 8x
f''(x) = 7x2 - 8x
172.
Differentiate the function: y = 4π2
a)
y' = 16
b)
y' =0
c)
y' = π
173.
Find the value of the limit
a)
1
b)
0
c)
4
d)
-1
174.
Find the value of the limit
a)
1
b)
0
c)
e
d)
sin(1)
175.
Find the value of the limit
a)
1/8
b)
8
c)
-8
d)
2/3
176.
Find the value of the limit
a)
0
b)
1/2
c)
sin(1)
d)
1
177.
Find the value of the limit
a)
pos. infinity
b)
DNE
c)
1
d)
2
178.
Find the value of the limit
a)
1
b)
2
c)
0
d)
5
179.
Find the value of the limit
a)
3
b)
-1
c)
3/2
d)
2/3
180.
Find the value of the limit
a)
1
b)
0
c)
infinity
d)
DNE
181.
Find the value of the limit
a)
1
b)
1/2
c)
2
d)
-1
182.
Find the value of the limit
a)
1
b)
1/3
c)
3
d)
-1/3
183.
a)
3
b)
-4
c)
8
d)
4
184.
a)
1/2
b)
1/4
c)
-1/4
d)
2
185.
a)
0
b)
DNE
c)
2
d)
-2
186.
a)
1/8
b)
1/3
c)
1/16
d)
9
187.
a)
-1/4
b)
-1/6
c)
-1/3
d)
-1/2
188.
a)
positive infinity
b)
0
c)
negative infinity
d)
DNE
189.
a)
2
b)
9
c)
4
d)
8
190.
a)
1/5
b)
-1/2
c)
-1/4
d)
4/5
191.
a)
1/3
b)
1/4
c)
-1/4
d)
-1/2
192.
a)
a = 10
b)
a = 4
c)
a = 15
d)
a = 11
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