Wednesday, october 25th “Consider the postage stamp:  its usefulness consists in the ability to stick to one thing till it gets there.” ~Josh Billings Score 2.8 Lesson 3.2 Reminders

Lesson 3.1 Scoring Guidelines 5 Limit done both ways 7 Slope of secant; is it larger or smaller than f’(2)? 9 Estimate f’(1) and f’(2) 13 Which is larger? 19 Find derivative; then write equation of tangent line 35 Find derivative using limit process 49 Intervals on which derivative is positive 51 Find f(x) and a 56 59 A. B.

The Derivative as a Function Lesson 3.2 The Derivative as a Function

Generalizing for all x … Section 3.1, Figure 3 Page 102

Using the definition

Ready for a shortcut? The Power rule:

Find each derivative using the power rule.

To which of the following does the Power rule apply?

Complete the table below for y’. x -4 -3 -2 -1 1 2 3 4 y’ 1 2 3 4 y’ 6 2.5 -1.5 -2 -1.5 2.5 6 6 -6

The value of the derivative and what it tells me about f(x) f’(x) is positive f’(x) is zero f’(x) is negative Slope of the tangent line to f is positive Slope of the tangent line to f is zero Slope of the tangent line to f is negative f has a horizontal tangent line at that point f is increasing at that point f is decreasing at that point

The value of the derivative and what it tells me about f(x) f’(x) is positive f’(x) is zero f’(x) is negative Slope of the tangent line to f is positive Slope of the tangent line to f is zero Slope of the tangent line to f is negative f has a horizontal tangent line at that point f is increasing at that point f is decreasing at that point

Not all functions have a derivative at every single point! When the limit exists, we say that the function is differentiable at a.

A function is NOT DIFFERENTIABLE if the graph has these characteristics: Discontinuity Sharp Turn Vertical Tangent Line