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# Second Derivatives and Beyond

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# Local vs. Global Points Exercises

### Example 1

Determine if the function has a global maximum and/or a global minimum.

### Example 2

Determine if the function has a global maximum and/or a global minimum.

### Example 3

Determine if the function has a global maximum and/or a global minimum.

### Example 4

Determine if the function has a global maximum and/or a global minimum.

### Example 5

Determine if the function has a global maximum and/or a global minimum.

### Example 6

Determine if the function has a global maximum and/or a global minimum.

### Example 7

Determine if the function has a global maximum and/or a global minimum.

### Example 8

Determine if the function has a global maximum and/or a global minimum.

### Example 9

Find the global max and global min of the function on the specified interval.

on the interval [-1,1]

### Example 10

Find the global max and global min of the function on the specified interval.

*f* (*x*) = *x*^{2} + 3*x* on the interval [-2,3]

### Example 11

Find the global max and global min of the function on the specified interval.

*f* (*x*) = *xe*^{x} on the interval [-2,-1]

### Example 12

Find the global max and global min of the function on the specified interval.

*f* (*x*) = sin *x* on the interval [π,2π]

### Example 13

Find the global max and global min of the function on the specified interval.

### Example 14

Find *where* the global max and global min of the function occur (on the specified interval).

*f* (*x*) = *x*^{2}*e*^{x} on the interval [-5,1]

### Example 15

Find *where* the global max and global min of the function occur (on the specified interval).

*f* (*x*) = 2*x*^{2} + 3*x* - 2 on the interval [-2,2]

### Example 16

Find *where* the global max and global min of the function occur (on the specified interval).

on the interval [-π,π]

### Example 17

Find *where* the global max and global min of the function occur (on the specified interval).

on the interval [-1,4]

### Example 18

Find *where* the global max and global min of the function occur (on the specified interval).

*f* (*x*) = 3(*x* - 2) + 9 on the interval [-5,5]