If the sum of two positive numbers x and y is 3, then the absolute maximum of x^3+12xy is what?

32 at x = 2

Step-by-step explanation:

If the sum of two positive numbers x and y is 3, then

and

To find the absolute maximum of the function

find the derivative

and equate it to 0:

For - the function f(x) increases

For - the function f(x) decreases

For - the function f(x) increases

So, x = 2 is maximum, x = 6 is minimum

The maximum value of is