Maximize and minimize.

Question

consider two nonnegative numbers x and y such that x+y=10. Maximize and minimize the quantities.

x^2y^2

Answer 1

minimum x^2y^2 is either x=0 y=10 or x=10, y=0

then x^2y^2 = 0

maximum is when x=y=5

then x^2y^2 = 25(25) = 625