## The Definition of a Derivative

Read this section to understand the definition of a derivative. Work through practice problems 1-8.

**Definition of Derivative:** if the limit exists and is finite.

**Tangent Line Equation:** The line is tangent to the graph of at .

(proven for = positive integer: true for all constants )

Slope of a line tangent to a graph

Instantaneous rate of change of a function at a point

Velocity or acceleration

Magnification factor

Marginal change