Consider the function p:R→R defined by p(x)=x1/3+x.
a. Establish that p is continuous at x=0.
b. Determine whether p is differentiable at x=0. Support your answer by computing the relevant limit or limits.
c. 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.