1. Lesson 3.2 Differentiability AP Calculus Mrs. Mongold

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

3. Derivatives Don’t Exist at… Corners: LHD ≠ RHD Cusp: LHD ≠ RHD or in extreme cases where the slopes of the lines approach ±∞ Vertical Tangent, where slopes approach ±∞ from both sides Discontinuity: when one or both of the one-sided derivatives do not exist

4. Differentiability Implies Local Linearity This means that the function at point a closely resembles it’s own tangent line very close to a. Curves will “straighten out” when we zoom in on them at a point of differentiability

5. Our Calculators Can Help Us

6. Example

7. Use your calculator to answer if either of these functions are differentiable at x = 0 f(x) = |x| +1 and g(x) =

8. Homework Book page 111/1-10, 17-22, 23, 30