Prove that value of the function `xy(y-x)=2a^3` is minimum at `x=a.`

Prove that the minimum value of the function x^(3)+(1)/(x^(3)) is greater than its maximum value.

For what values of x, the function f(x) = x^(5)-5x^(4)+5x^(3)-1 is maximum or minimum? Prove that at x = 0, the function is neither maximum nor minimum.

For what values of x, the function f(x) = x^(5)-5x^(4)+5x(3)-1 is maximum or minimum? Prove that at x = 0, the function is neither maximum nor minimum.

Prove that the function f(x) = 2x^3 - 6x^2 + 6x + 5 has no maximum or minimum.

The complete graph of the function f is shown in the xy-plane above. For what value of x is the value of f(x) at its minimum?

Show that the function 2x^(3)+3x^(2)-36x+10 has a maximum value at x=-3 and a minimum value at x=2 , also find the maximum and minimum values of the function.

The minimum value of the function y = |2x+1| + 2|x-2| , is

The minimum value of the function y = |2x+1| + 2|x-2| , is

If xy(y-x)=16 then y has a minimum value when x=