# Derivatives

### Example 1

For the given function *f *andvalue *a, *find the tangent line to *f *at* a. *

*f*(*x*)*= x*+^{2}*, a*= 1

### Example 2

For the given function *f* and value *a*, find the tangent line to *f* at *a*.

*f*(*x*) =*x*^{2}+ 1,*a*= 0

### Example 3

For the given function *f* and value *a*, find the tangent line to *f* at *a*.

*f*(*x*) =*x*^{3}, a = 1

### Example 4

For the given function *f* and value *a*, find the tangent line to *f* at *a*.

*f*(*x*) = 1-*x*^{2}, a = -1

### Example 5

For the given function *f* and value *a*, find the tangent line to *f* at *a*.

### Example 6

For the function *f* and value of *a*, use the magic formula to find the tangent line to *f* at *a*. We will need to calculate derivatives from scratch.

*f*(*x*) = 2*x*+ 3*x*^{2},*a*= 4

### Example 7

For the function *f* and value of *a*, use the magic formula to find the tangent line to *f* at *a*. We will need to calculate derivatives from scratch.

*f*(*x*) = 2*x*^{3},*a*= -2

### Example 8

For the function *f* and value of *a*, use the magic formula to find the tangent line to *f* at *a*. We will need to calculate derivatives from scratch.

*
*

### Example 9

The graph shows a function *f* and a line that is tangent to *f* at *a*. For the graph determine *a*, *f*(*a*), and *f'*(*a*) (*a* refers to the *x*-value at which the line is tangent to *f*).