1. 2.1B Derivative Graphs & Differentiability

2. Differentiation Operators:

3. f is differentiable at a if f (a) exists.
If f is differentiable at a, then f is continuous at a. (*NOT vice versa)

4. f is NOT differentiable at a.x y
1) At a corner or cusp

5. f is NOT differentiable at a.x y
2) At a discontinuity

6. f is NOT differentiable at a.x y
3) Vertical Tangent Line

7. Ex 1: Compare the graphs of f (x) & f (x) .

8. Ex 2:
Sketch the graph of the function g for which g(0) = 0, g(0) = 3, g(1) = 0, & g(2) = 1.

9. Ex 3: If the tangent line to f (x) at (3, 6) passes through the point (1, 2), find f (3) & f (3).

10. HW – 2.1B pg.104 # 37 – 48 all, # 53 – 56 all, 59, # 81 – 95 odds