# Derivatives

# Tangent Lines and Derivatives Exercises

### Example 1

For the function *f* and value *a*, determine if *f'*(*a*) is positive, negative, or zero.

### Example 2

For the function *f* and value *a*, determine if *f'*(*a*) is positive, negative, or zero.

### Example 3

For the function *f* and value *a*, determine if *f'*(*a*) is positive, negative, or zero.

### Example 4

For the function *f* and value *a*, determine if *f'*(*a*) is positive, negative, or zero.

### Example 5

For the function *f* and value *a*, determine if *f'*(*a*) is positive, negative, or zero.

### Example 6

- For the function shown below, which is greater:
*f*'(*x*_{1}) or*f*'(*x*_{2})?

### Example 7

- For the function shown below, which is greater:
*f*'(*x*_{1}) or*f*'(*x*_{2})?

### Example 8

- For the function shown below, list in order from least to greatest:
*f*'(*x*_{1}),*f*'(*x*_{2}),*f*'(*x*_{3}).

### Example 9

- For the function shown below, list in order from least to greatest:
*f*'(*x*_{1}),*f*'(*x*_{2}),*f*'(0).