2.7 Nondifferentiable Functions

Nondifferentiable Functions

Thus far we have learned to find derivatives by the definition of derivative, the Power Rule, the Sum & Difference Rules, the Product Rule, the Quotient Rule, and the Chain Rule. However, there are functions that cannot be differentiated at certain values. These are called nondifferentiable functions. Knowing where a function is not differentiable is the focus of this section.

Summary of Nondifferentiable Functions

Therefore, if a function f satisfies any of the following conditions:

1. f has a corner point at x = c,

2. f has a vertical tangent at x = c,

3. f is discontinuous at x = c, then f will not be differentiable at c.

Nondifferentiable Functions at c

A.1 Graph f(x) = | x | and show it's not differentiable at x = 0.

A.2: Find the x-values at which the derivative is undefined.