Answer
a. See graph,
b. no vertical tangent.
Work Step by Step
a. See graph; it appears to have a vertical tangent at $x=0$
b. Evaluate the limit: $\lim_{h\to0}\frac{f(0+h)-f(0)}{h}=\lim_{h\to0}\frac{h^{2/5}-0}{h}=\lim_{h\to0}\frac{1}{h^{3/5}}=$ As $\lim_{h\to0^+}\frac{1}{h^{3/5}}=\infty$ and $\lim_{h\to0^-}\frac{1}{h^{3/5}}=-\infty\ne \lim_{h\to0^+}\frac{1}{h^{3/5}}$, thus there is no vertical tangent at this point.
