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Worksheet: Local Extrema in Graphs of Functions

In this worksheet, we will practice finding critical points and local or absolute extreme values (maxima and minima) using the graph of the function.

Q1:

Find the maximum and minimum values of the function , where .

A maximum value: , minimum value:
B maximum value: , minimum value:
C maximum value: , minimum value:
D maximum value: , minimum value:
E maximum value: , minimum value:

Q2:

Determine the number of local extrema for the function .

Q3:

Which graph has three real zeros and two local maxima?

A
B
C

Q4:

Using a graphing calculator to graph the function, find and classify all the extreme points of . If necessary, round any values to 2 decimal places.

ALocal minimum: , local maximum:
BLocal minimum: , local maximum:
CLocal minimum: , local maximum:
DLocal minimum: , local maximum:

Q5:

Determine the local maximum and minimum values of the function .

Alocal maximum value
Blocal minimum value, local maximum value
Clocal minimum value
Dlocal maximum value, local minimum value
Elocal minimum value

Q6:

Find the values of the local maximum and minimum of given .

Athe local maximum value is , the local minimum value is
Bthe local maximum value is , the local minimum value is
Cthe local maximum value is , the local minimum value is
Dthe local maximum value is , the local minimum value is
Ethe local maximum value is , the local minimum value is

Q7:

Determine the number of local extrema for the function .