# Math 22 The Derivative and the Slope of a Graph

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## Slope of a Graph

We can estimate the slope at the given point to be

Slope =

## Difference Quotient

The slope of the graph of at the point can be written as : The right side of this equation is called Difference Quotient

Example: Find the Different Quotient of

**1)**

Solution: Consider

**2)**

Solution: |
---|

Consider |

## Definition of the Derivattive

The derivative of at is given by provided this limit exists. A function isdifferentiableat when its derivative exists at . The process of finding derivatives is calleddifferentiation.

Example: Use limit definition to find the derivative of

**1)**

Solution: Consider:

**2)**

Solution: |
---|

Consider: |

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