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WorksheetsUnit 6- Week 3- First Derivative Test
Total questions: 10
Worksheet time: 18mins
Name
Class
Date
1.
Refer to the graph and the information below.
The function f is defined on the closed interval [0,8]. The graph of its derivative f' is shown above.
At what value of x does the absolute minimum of f occur?
a)
0
b)
2
c)
4
d)
6
e)
8
2.
The figure shows the graph of f′, the derivative of a function f. The domain of f is the set of all real numbers x such that −3 < x < 5.
For what values of x does f have a relative maximum?
(a)
3.
Over what interval(s) is f(x) increasing?
a)
(-∞, -3) ∪ (1, ∞)
b)
(-3, 1)
c)
(-5, 0) ∪ (2, ∞)
d)
(-5, ∞)
4.
If a function's FIRST derivative is negative at a certain point, what does that tell you?
a)
The function is increasing at that point
b)
The function is decreasing at that point
c)
The concavity of the function is up at that point
d)
The concavity of the function is down at that point
5.
The slope of a function is described by its ____________.
a)
first derivative
b)
second derivative
c)
third derivative
d)
expression
6.
Use the sign chart for f'(x). There is(are) ...
a)
a local maximum at x = -2.
b)
a local minimum at
x = -2 and a local maximum at x = 4.
x = -2 and a local maximum at x = 4.
c)
a local maximum at
x = -2 and a local minimum at x = 4.
x = -2 and a local minimum at x = 4.
d)
no extrema.
7.
Over what intervals is f(x) decreasing?
a)
(-∞, -1) ∪ (1, ∞)
b)
(-∞, -√3) ∪ (0, √3)
c)
(-1, 1)
d)
(-√3, 0) ∪ (√3, ∞)
8.
a)
-1 , 0 , -1.5
b)
-1 , 0
c)
-1 , 2/3
d)
-1 , 0 , 1.5
9.
Find the second derivative of the function:
f (x) = 2x - 5x6
f (x) = 2x - 5x6
a)
f ''(x)= 2 - 30x
b)
f ''(x) = 2-30x5
c)
f ''(x) = -30x5
d)
f ''(x) = -150x4
10.
Find the derivative of y = 2x2 (3x - 4)
a)
6x3 - 8x2
b)
18x2 - 16x
c)
15x2 - 6x
d)
6x - 4
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