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: $\lim_{h\to0}\frac{f(0+h)-f(0)}{h}=\lim_{h\to0}\frac{4h^{2/5}-2h}{h}=\lim_{h\to0}(h^{-3/5}-2)$.
As $\lim_{h\to0^+}(h^{-3/5}-2)=\infty$ and $\lim_{h\to0^-}(h^{-3/5}-2)=-\infty\ne \lim_{h\to0^+}(h^{-3/5}-2)$, the function does not have a vertical tangent at $x=0$
