One-sided derivatives The right-sided and left-sided derivatives of a function at a point...

One-sided derivatives The right-sided and left-sided derivatives of a function at a point a are given by , respectively, provided these limits exist. The derivative f′(a) exists if and only if f+′(a) = f−′(a).

a. Sketch the following functions.

b. Compute f+′(a) and f−′(a) at the given point a.

c. Is f continuous at a? Is f differentiable at a?

f(x) = |x − 2|; a = 2