Find the absolute maximum value and the absolute minimum value, if any, of the function.

g(x)=x^2+9x^2/3 on [-7,8]

I assume you mean x^2 + 9x^(2/3) or the formula is a bit odd.

f(-7) = 81.93
f(8) = 100

f(0) = 0, and f(x) >=0 for all x

absolute min is thus 0
absolute max on [-7,8] = 100