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

Show that , the maximum value of the function x+(1)/(x) is less than its minimum value .

Show that a local minimum value of f(x) = x + 1/x , x ne 0 is greater than a local maximum value.

Show that , the maximum value of the function (1)/(3)x^(3)-2x^(2)+3x+1 is (4)/(3) more than its minimum value.

Investigate for what values of x, the fuction (x-1)/(x^(2)+x-1) is a maximum or minimum .also show that the maximum value of the fuction is less than its minimum value

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

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

The maximum and minimum values of the function |sin 4x+3| are

Find the maximum or minimum value of the function (sin x)/(1+tan x)

Prove that,maximum and minimum values of the function x^(3)-18x^(2)+96x in the interval (0,9) are given by 160 and 128 respectively.

Prove that maximum and minimum values of the function x^(3)-18x^(2)+96x in the interval (0,9) are given by 160 and 128 respectively.