Question

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

Answer 1

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

Answer 2

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

Answer 3

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)

Answer 4

im confused.

Answer 5

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

Answer 6

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)