1. 3.2: Differentiability

2. Most of the functions we study in calculus will be differentiable.
If f has a derivative at x = a, then f is continuous at x = a.
However, if a function is continuous at x=a, it is not necessarily differentiable at x=a!
Continuous, but NOT Differentiable at x=0!

3. To be differentiable, a function must be continuous and smooth.
Derivatives will fail to exist at:
corner
cusp
discontinuity
vertical tangent

4. Derivatives on the Calculator

5. p Intermediate Value Theorem for Derivatives
If a and b are any two points in an interval on which f is differentiable, then takes on every value between and
Between a and b, must take on every value between and . p

6. Homework
p. 114 #1-35 odd