F=x^3(40-x)^2 F=x^3(1600-80x+x^2) F=x^5-80x^4+1600x^3 F'=5x^4-320x^3+4800x^2 At the max. F'=0 5x^4-320x^3+4800x^2=0 B (Divide by 5) X^4-64x^3+960x^2=0 X^2 (x^2-64x+960)=0 X^2 (x-24)(x-40)=0 x=0 or x= 24 or x=40 y=40 or y=16 or y=0 x=24, y=16 are the two integers which satisfy the problem