$\displaystyle f(x)=x^\frac{4}{5}(x-4)^2$

find the critical numbers of the function:

$\displaystyle f'(x)=\frac{4}{5}x^\frac{-1}{5}(x-4)^2 + 2(x-4)(x^\frac{4}{5})

$

factor a term out:

$\displaystyle x^\frac{-1}{5}(\frac{4}{5}(x-4)^2 + 2x^\frac{5}{5}(x-4))$

I see the 0 and 4, but the solution guide says there is also a critical number at $\displaystyle \frac{8}{7}$.