DEFINITION OF THE DERIVATIVEDerivatives Review- 1

Tangent Line Problem

The tangent line can be found by finding the slope of the secant line through the point of tangency and a point on the curve

Theorem 2-1

Differentiability implies continuity

Not the other way around

For a function f(x) the average rate of change along the function is given by:

Which is called the derivative of f

f '(x) lim

x 0f (x x) f (x)

x

Definition of the Derivative

Notation:

1) Find the derivative using the limiting process

f (x) x 2 3x

2) Find the equation of the tangent line through the point (-2 , 2)

f (x) x 2 3x 4

Graphs and their derivatives

3) The graph of f(x) is given. Sketch the graph of f’

4) Piecewise derivatives.

a) Find f’(3)

b) Find f’(4)

c) Find f’(0)

3 x9-6x

3 x )(

2xxf

HOME WORKPage 104 # 5-23 odd and # 39-48 and Worksheet 2-A derivatives