1. 2.1 Tangent Line Problem

2. 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 Point A is the point of tangency

3. Tangent Line Problem How to find slope of a curve at a point? xx + Δx Secant Line Tangent Line

4. xx + Δx Setting up a limit! Slope of the Tangent Line

5. 1.) Find slope of the secant line x x + Δx Secant Line

6. xx + Δx Called the difference quotient Conclusion:

7. For a function f(x) the average rate of change along the function is given by: Which is called the derivative of f Definition of the Derivative

8. Notation of the Derivative The derivative of a function at x is given by: **Provided the limit exists Notation:

9. 2.) Find the slope of the tangent line to the curve at (2,6) First, find the Slope at any point

10. Terminology Differentiation (Differentiate) – the process of finding the derivative Differentiable – when a functions derivative exists at x

11. When Derivatives Fail 1.Cusp or sharp point: cusp

12. When Derivatives Fail 2.Vertical asymptotes: 3.When one sided limits fail

13. When Derivatives Fail 4.Removable discontinuity

14. When Derivatives Fail 5. Corners or vertical tangents

15. 3.) Differentiate (if possible)

16. 4.) Differentiate (if possible)

17. 5.) Differentiateif possible

18. 6.) Find the derivative of

19. HOMEWORK Page 104 # 5 – 21 (odd), 61 and 62, 83-88 (all). Find where f(x) is not differentiable and state the type of discontinuity