WorksheetsUsing Derivatives to Graph Function
Total questions: 15
Worksheet time: 34mins
Name
Class
Date
1.
Let f be the function with derivative given by f'(x) = sin(x2 + 1). How many relative extrema does f have on the interval 2 < x < 4?
a)
Two
b)
Three
c)
Four
d)
Five
2.
Let f be the function with derivative given by f'(x) = x2 - 2/x. On which of the following intervals is f decreasing? (No Calculator)
a)
(-∞, 0]
b)
(-1, 0]
c)
(0, ∛2]
d)
(∛2, ∞)
3.
Given a function, f(x), if f'(x)<0 over a certain interval, then f(x) is ____________ over that interval.
a)
decreasing
b)
increasing
c)
concave up
d)
concave down
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.
For a function g(x), g'(-2)=0 indicates that x=-2 is ________________.
a)
an inflection point
b)
a critical point
c)
a relative maximum
d)
a relative minimum
7.
For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.
a)
increasing
b)
decreasing
c)
concave up
d)
concave down
8.
The slope of a function is described by its ____________.
a)
first derivative
b)
second derivative
c)
third derivative
d)
expression
9.
Find the critical points of f(x) = 2x4- 4x2 + 1
a)
x= 0
b)
x = -1, 1
c)
x = -1, 0, 1
d)
no critical points
10.
What are the intervals of the graph increasing for f(x) = 2x4- 4x2 + 1
a)
(-1,0)
b)
(0,1)
c)
(-∞,-1) and (1,∞)
d)
(0,1) and (-1,0)
11.
If given f'(x) how would you find the intervals which the graph f(x) has a positive slope?
a)
f'(x) < 0 (negative)
b)
f'(x) > 0 (positive)
c)
f'(x) is increasing
d)
Can't be determined
12.
What is the maximum value of f(x) = x3 - 3x2 - 1 on the interval [-3, 2]?
a)
0
b)
-1
c)
2
d)
5
13.
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
14.
f' is given, which could be f?
a)
A
b)
B
c)
C
15.
Select the correct derivative of f(x).
a)
A.
b)
B.
c)
C.
d)
D.
100 %
