question number eleven

Question

Find the absolute maximum and absolute minimum values of the function below. If an absolute maximum or minimum does not exist, enter NONE.

 on the open interval (0, )

Answer 1

f'(x) = 2x - 128/x² = 0; 2x³ - 128 = 0; x = 4

f''(x) = 2 + 256/x³; f''(4) = 2 +, 256/64 = 6 > 0.

So, at x = 4 function has absolute min f(4) = 4² + 128/4 = 48