Find the maximum value of the function `x * e^(-x)`.

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

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

Examine the following functions for maxima and minima : Find the maximum value of the function f(x)=x-e^(x) .

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 f(x)=x^(-4)e^(-(2)/(x)) , x>0

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

Find the maximum value of the function (x^(2)+14x+9)/(x^(2)+2x+3) over R.

Find the maximum value of the function 2x^(3)+3x^(2)-36x+10 .

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