1. Section 3.2 Differentiability

2. Ways a function might not be differentiable.  1. a corner  Often occurs with absolute value functions.

3. Ways a function might not be differentiable.  2. A cusp.  Often seen when a function has a rational exponent… x 2/3.

4. Ways a function might not be differentiable.  3. A vertical tangent.  Example: Cube root function.

5. Ways a function might not be differentiable.  4. A discontinuity.

6. Differentiable vs. Continuous  Differentiability implies local linearity.  A function starts to look like its tangent line when you zoom in very close.  If a function is differentiable, then it is continuous. The converse, however, is not necessarily true.

7. Derivatives on the Calculator  Math – 8 (nderiv)  Tell the calculator the variable, the function, and the value at which you are evaluating the derivative. You can enter x=x instead of a value if you want to graph the derivative.