Question

The sum of two positive integers x and y is 90. Find the value of x that minimizes P=x^3-90xy. (Only an algebraic solution is accepted.)

Answer 1

x+y=90
so put y=90-x into function
derive it
f'=0
find roots
find min

Answer 2

Do I take the derivative of x^3-90xy then find the roots of that?

Answer 3

f(x,y)=x^3-90xy
apply y=90-x
so
f(x)=x^3-90x(90-x)
then find f'=0 roots

Answer 4

the roots of f'=0 must be -30 ,90
f=3x^2-180x+90^2