Showing a vertical tangent exists at a given function. I want to apologise in advance for not having this in latex or some sort of neat code, I would be more than happy to learn how though.
Anyway, for the function $y=4(x-1)^{2/5}$ I see there appears to be a vertical tangent at $x=1$, but how can I know for certain the vertical tangent exists at $x=1$? Would I just solve for $f'(x)$, letting $x=1$? But what would that tell me?
Thanks. 

Yes, you would check if $f'(1)$ tends to $+\infty$ or $-\infty$
$$
\frac{d}{dx}4(x-1)^{2/5}=\frac{8}{5}(x-1)^{-3/5}\\
$$
