Deck 4: Extension C: Applications of Differentiation

Question 1

The graph of the derivative of a continuous function f is shown.On what intervals is f decreasing?

A)
B)
C)
D)
E) None of these

Answer 1

Question 2

Determine where the graph of the function is concave upward and where it is concave downward.Also,find all inflection points of the function.

A) CU on , CD on ,
IP
B) CU on , CD on ,
IP
C) CU on , CD on ,
IP
D) CU on , CD on ,
IP

Answer 2

CU on , CD on ,
IP

Question 3

The graph of the first derivative of a function f is shown below.At what values of x does f have a local maximum or minimum?

Answer 3

3,5,8,10

Question 4

Given (a)Find the intervals on which f is increasing or decreasing. (b)Find the relative maxima and relative minima of

A) (a) Increasing on ,
Decreasing on
(b) Rel. max.
B) (a) Increasing on ,
Decreasing on
(b) Rel. min.
C) (a) Increasing on ,
Decreasing on
(b) Rel. max.
D) (a) Increasing on ,
Decreasing on
(b) Rel. min.

Question 5

Determine where the graph of is concave upward and where it is concave downward.Also,find all inflection points of the function.

A) concave downward: and , concave upward: and ; inflection points: and
B) concave downward: and , concave upward: and ; inflection points: and
C) concave downward: nowhere, concave upward: and ; inflection points: none
D) concave downward: and , concave upward: nowhere; inflection points: none

Question 6

Determine where the graph of the function is concave upward and where it is concave downward.Also,find all inflection points of the function.

A) CU on , CD on ,
IP
B) CU on , CD on and
IP and
C) CU on , CD on ,
IP
D) CU on , CD on ,
IP

Question 7

Given (a)Find the intervals on which f is increasing or decreasing. (b)Find the relative maxima and relative minima of

A) (a) Increasing on ,
Decreasing on
(b) Rel. max.
B) (a) Increasing on
(b) None
C) (a) Decreasing on
(b) None
D) (a) Increasing on ,
Decreasing on
(b) Rel. min.

Question 8

Estimate the extreme values of the function.Round the answers to the nearest hundredth.

Question 9

Given
(a)Find the intervals on which f is increasing or decreasing.
(b)Find the relative maxima and relative minima of

A) (a) Increasing on and , decreasing on
(b) Rel. max. ,
Rel) min.
B) (a) Increasing on and , decreasing on and
(b) Rel. max. ,
Rel) min.
C) (a) Increasing on , decreasing on and
(b) Rel. max. ,
Rel. min.
D) (a) Increasing on and decreasing on and
(b) Rel. max. ,
Rel. min.

Question 10

Find a cubic function that has a local maximum value of at 1 and a local minimum value of -1,184 at 7.

Question 11

Use the Second Derivative Test to find the relative extrema,if any,of the function

A) Rel. max. ,
Rel. min.
B) Rel. max. ,
Rel. min.
C) Rel. max. ,
Rel. min.
D) Rel. max. ,
Rel. min.

Question 12

Given (a)Find the intervals on which f is increasing or decreasing. (b)Find the relative maxima and relative minima of

A) (a) Increasing on and decreasing on
(b) Rel. max. ,
Rel) min.
B) (a) Increasing on , decreasing on and
(b) Rel. max. ,
Rel) min.
C) (a) Increasing on and decreasing on
(b) Rel. max. ,
Rel) min.
D) (a) Increasing on , decreasing on and
(b) Rel. max. ,
Rel. min.

Question 13

Determine where the graph of is concave upward and where it is concave downward.Also,find all inflection points of the function.

Question 14

Consider the function
(a)Find the intervals on which f is increasing or decreasing.
(b)Find the relative maxima and relative minima of F)

Question 15

Find the maximum or minimum point(s)of the function.

A)
B)
C)
D)
E)