I know to find the critical numbers you'd find the first derivative and solve for where it is 0, but I just can't get the right answer for this one
f(x)= x^(1/5) - x^(-4/5)
$\displaystyle f'(x)=\frac{1}{5x^{\frac{4}{5}}}+\frac{4}{5x^\frac {9}{5}}$
$\displaystyle 0=\frac{1}{5x^{\frac{4}{5}}}+\frac{4}{5x^\frac{9}{ 5}}$
$\displaystyle 0=\frac{1}{5x^{\frac{4}{5}}}(1+\frac{4}{x})$
What is the given answer? Because as far as I can tell, having checked, and having checked again, there's no problem with your work, unless I'm missing something.