If `x+y=1` then find the maximum value of the function `xy^2`

If x+y=a then find the maximum value of the function xy^(2)

Find the maximum value of the function x^(1//x) .

Find the maximum value of the function x^(1//x) .

Find the maximum value of the function 1//(x^(2)-3x+2) .

Find the maximum value of the function (x-1)(x-2)(x-3)

if 2x+y=1 then find the maximum value of x^(2)y

If x+y =12 what is the maximum value of xy?

Prove that at x=(pi)/(3), function sin x(1+cos x) is maximum.Also find the maximum value of the function.

Find the maximum and the minimum value of the function y=x^(3)+6x^(2)-15x+5