NEW
Font size
S
M
L
XL
WorksheetsApplication of derivatives
Total questions: 15
Worksheet time: 13mins
Name
Class
Date
1.
What is a horizontal tangent?
a)
Has a positive slope.
b)
Has a negative slope.
c)
Has a slope of zero.
d)
Has an undefined slope.
2.
What is a vertical tangent?
a)
Has a positive slope.
b)
Has a negative slope.
c)
Has a slope of zero.
d)
Has an undefined slope.
3.
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 constant
d)
Neither increasing nor decreasing
4.
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
5.
Does this graph have a maximum or minimum value?
a)
maximum
b)
minimum
c)
neither
d)
both
6.
How many extrema are in the picture?
a)
2
b)
3
c)
4
d)
5
7.
If f"(x) < 0, what is true about f(x)?
a)
it is concave up there
b)
it has an inflection point
c)
It's zero
d)
it is concave down there
8.
If f '(x) <0, what is true about f(x)?
a)
it is concave up there
b)
it's decreasing
c)
It's increasing
d)
it is concave down there
9.
What is the equation of the line tangent to y= x2+2x-1 at x=1?
a)
y=2x
b)
y=4x-2
c)
y=4x
d)
y=2x-2
10.
a)
-1/4
b)
1/4
c)
π/4
d)
-π
11.
What is a horizontal tangent?
a)
Has a positive slope.
b)
Has a negative slope.
c)
Has a slope of zero.
d)
Has an undefined slope.
12.
The velocity of an object is given as v = 2t + 3t3. what is the acceleration of the object at t = 2 s?
a)
38 m/s/s
b)
27 m/s/s
c)
16 m/s/s
d)
49 m/s/s
13.
If the position of a particle is represented by x(t) = -t2 + 1, what is its instantaneous velocity at t = 1?
a)
v = 0
b)
v = 1
c)
v = -1
d)
v = -2
14.
The radius of a circle is decreasing at a constant rate of 0.1 cm/sec. In terms of the circumference C, what is the rate of change of the area of the circle, in square centimeters per second?
a)
-(0.2)πC
b)
-(0.1)C
c)
(0.1)2C
d)
(0.1)2C
15.
Find the second derivative of
f(x) = x2 + ex - cosx
f(x) = x2 + ex - cosx
a)
f"(x) = 2 + ex + cosx
b)
f"(x) = 2x + ex + cosx
c)
f"(x) = 2x + xex - cosx
d)
f"(x) = 2x + ex + sinx
Reset
