# Second Derivatives and Beyond

### 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*) = *e*^{x}sin *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*) = *x*^{3} – 2*x*^{2} + *x*

### Example 4

### Example 5

### 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*) = *x*^{4} - 32*x*

### 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 to use the test you did.

*f* (*x*) = (*x* - 1)^{9}

### Example 9

*f* (*x*) = *e*^{x2 - 4x}