find two non-negative numbers x and y whose sum is 100 and for which x^2y is a maximum

Question

anonymous · Answer

replace y by $100-x$ and find the maximium of $x^2(100-x)$

anonymous · Answer

do i take the derivate of the x^2(100-x)

anonymous · Answer

yes, but i would multiply out first and get 
$$f(x)=100x^2-x^3$$ derivative is easy right? then find the critical points in the interval (0,100)

anonymous · Answer

im confused.

anonymous · Answer

i just suggested to multiply out before you take the derivative to make it easier

anonymous · Answer

we already know our function is $f(x)=x^2(100-x)$ i just suggested to start with 
$$f(x)=100x^2-x^3$$ because it is easier to take the derivative that way
you get 
$$f'(x)=200x-3x^2$$ and now it is easy enough to find the zeros (critical points)