Wednesday , october 25th

1. 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

2. Lesson 3.1 Scoring Guidelines

3. Lesson 3.2 The Derivative as a Function

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

5. Using the definition

6. Ready for a shortcut? The Power rule:

7. Find each derivative using the power rule.

9. To which of the following does the Power rule apply?

10. 11. Let Complete the table below for y’. -1.5 -1.5 6 -2 2.5 6 2.5 0 0 6 -6

11. The value of the derivative and what it tells me about f(x) f’(x) is zero f’(x) is positive 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

12. The value of the derivative and what it tells me about f(x) f’(x) is zero f’(x) is positive 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

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

14. A function is NOT DIFFERENTIABLE if the graph has these characteristics: