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Second Derivative Test Exercises

Example 1

For the function, use the second derivative test (if possible) to determine if each critical point is a minimum, maximum, or neither. If the second derivative test can't be used, say so.

Example 2

For the function, use the second derivative test (if possible) to determine if each critical point is a minimum, maximum, or neither. If the second derivative test can't be used, say so.

f (x) = exsin x for 0 < x < 2π

Example 3

For the function, use the second derivative test (if possible) to determine if each critical point is a minimum, maximum, or neither. If the second derivative test can't be used, say so.

f (x) = x3 – 2x2 + x

Example 4

For the function, use the second derivative test (if possible) to determine if each critical point is a minimum, maximum, or neither. If the second derivative test can't be used, say so.

Example 5

For the function, use the second derivative test (if possible) to determine if each critical point is a minimum, maximum, or neither. If the second derivative test can't be used, say so.

f(x) = cos x on the interval

Example 6

Classify the extreme points of the function, using either the first or second derivative test. Explain why you chose to use the test you did.

f (x) = x4 – 32x

Example 7

Classify the extreme points of the function, using either the first or second derivative test. Explain why you chose to use the test you did.

f (x) = (x – 1)9

Example 8

Classify the extreme points of the function, using either the first or second derivative test. Explain why you chose the test that you did. 

Example 9

Classify the extreme points of the function, using either the first or second derivative test. Explain why you chose to use the test you did.

f (x) = ex2 – 4x

Example 10

Classify the extreme points of the function, using either the first or second derivative test. Explain why you chose to use the test you did.

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