MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Consider the function p:R→R defined by p(x)=x1/3+x.
(1) Establish that p is continuous at x=0.
(2) Determine whether p is differentiable at x=0. Support your answer by computing the relevant limit or limits.
(3) Describe the behavior of the tangent to the graph of p near x=0 and classify the type of non-differentiability (if any) present at that point.