Lesson 3.2 Differentiability AP Calculus Mrs. Mongold.

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Presentation transcript:

Lesson 3.2 Differentiability AP Calculus Mrs. Mongold

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

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

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

Our Calculators Can Help Us

Example

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

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