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WorksheetsCalculus Review - Applications of Derivatives
Total questions: 15
Worksheet time: 39mins
Name
Class
Date
1.
If the position function for a particle is s(t) = -t2 - t, what is the instantaneous velocity function for the particle?
a)
v(t) = -2
b)
v(t) -2t - 1
c)
v(t) = t3
d)
v(t) = -t
2.
Where does the function, f(x) = 2x3 - 9x2 + 12x -3 have relative max/min values?
a)
Rel max x = -1, Rel min x = 2
b)
Rel min x = 1, Rel min x = 2
c)
Rel max x = 1, Rel min x = 2
d)
Rel max x = 2, Rel min x = 1
3.
Let f be the function with derivative given by f'(x) = x2 - 2/x. On which of the following intervals is f decreasing?
a)
(-∞, 0]
b)
(-1, 0]
c)
(0, ∛2]
d)
(∛2, ∞)
4.
Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.
a)
increasing
b)
decreasing
c)
concave up
d)
concave down
5.
Given a function g(x), if g'(x)=0 at a certain value of x, then g(x) has _____________ at x.
a)
an inflection point
b)
a critical point
c)
a minimum
d)
a maximum
6.
The slope of a function is described by its ____________.
a)
first derivative
b)
second derivative
c)
third derivative
d)
expression
7.
What is the maximum value of f(x) = x3 - 3x2 - 1 on the interval [-3, 2]?
a)
0
b)
-1
c)
2
d)
5
8.
If a function has a derivative that is negative, what does that tell you?
a)
The function is increasing
b)
The function is decreasing
c)
The function is concave up
d)
The function is concave down
9.
What is a point of inflection?
a)
When a function goes from increasing to decreasing
b)
When a function goes from concave up to concave down
10.
If a function has a second derivative that is negative, what does that tell you?
a)
The function is increasing
b)
The function is decreasing
c)
The function is concave up
d)
The function is concave down
11.
If a function has a second derivative that is positive, what does that tell you?
a)
The function is increasing
b)
The function is decreasing
c)
The function is concave up
d)
The function is concave down
12.
Over what interval(s) is f(x) decreasing?
a)
(-3, 1)
b)
(-∞, -5) ∪ (0, 2)
c)
(-∞, -3) ∪ (1, ∞)
d)
(-5, 0) ∪ (2, ∞)
13.
The derivative f'(x) of the function f(x) is shown. On what interval(s) is the FUNCTION f(x) increasing?
a)
(-∞, -1) only
b)
( 3, ∞) only
c)
(-∞, -1) and ( 3, ∞)
d)
(1, ∞)
14.
Find the x-coordinate of the inflection point of f(x)=6x2-x3.
a)
-2
b)
0
c)
2
d)
None
15.
A rectangular solid that has a square base has a surface area of 150 square inches. Find the maximum volume of the solid. (use Calculus)
a)
5
b)
125
c)
150
d)
250
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