1. Differentiability Notes 3.2

2. I. Theorem If f(x) is differentiable at x = c, then f(x) is continuous at x = c. NOT VICE VERSA!!! A.) Ex. - Continuous at x = 0, but not differentiable

3. II. Where the Derivative Does Not Exist The derivative fails to exist at x = c if… A.) there is a “corner” at x = c. B.) there is a vertical tangent at x = c. C.) there is a discontinuity at x = c.

4. Ex. – Prove f’(x) for the following does not exist at x = 0.

5. III. Symmetric Difference Quotient Nderiv on TI-83+/TI-84 Symmetric Diff. Quot. ≠ Limit Def. of Derivative

6. IV. Graphing with nderiv Place in Y8- ndeiv (Y1, x, x) Try