f(x) = (x-2)^3 / x^2
find the relative max and min.
so obviously i would bring the x^2 up.
this is what i have so far,
^{=}_{ x^2(x-2)^3-(x-2)^3(x^2) =x^2(3)(x-2)^2-(x-2)^3(2)(x) }is this correct so far?
We are given the function:
$\displaystyle f(x)=\frac{(x-2)^3}{x^2}$
Using the quotient rule, we find:
$\displaystyle f'(x)=\frac{x^2(3(x-2)^2)-2x(x-2)^3}{(x^2)^2}=\frac{x(x-2)^2(3x-2(x-2))}{x^4}=\frac{(x-2)^2(x+4)}{x^3}$