Find the maximum and minimum values of Given function

Assume a function 
F(x) = (sin −1 x)+(cos −1 x) ³

Then find F'(x) and F"(x) .

Calculate The point (x=?) for Maxima/Minima F' (0) = 0.

Put the calculated value of x [ From F' (0) =0 ] to the equation F" (x) to check the condition for maxima.

Now you get the value of x for which F(x) is maximum.

Put that value of x [for maxima] in F(x) to get maximum value of (sin −1 x)+(cos −1 x)³ .

Here you may apply the formula (sin −1 x) + (cos −1 x) = pi / 2 .