Find the absolute maximum value and the absolute minimum value

Question

Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.)

g(x) = x² + 5x^2/3 on [0,1]

Max=

Min=

Answer 1

Derivative g'(x) = 2x + 10/3x^-1/3 > 0 for x > 0 and f(x) is increasing. And only at x = 0 derivative DNE, so we have critical number. We evaluate f(0) = 0 is absolutee min and f(1) = 1 + 5 = 6 is absolute max