Find the local max and min values of the function: f(x) = x^3 / 3 - 3x^2 + 16x + 4, if they exist.?

Question

Thanks for any help! Greatly Appreciated.

Answer 1

f(x) = (1/3)x^3 - 3x^2 + 16x + 4
f '(x) = (1/9)x^2 - 6x + 16 = 0
x^2 - 54x + 144 = 0
x = (-b +/- √(b^2 - 4ac))/2a
x = (54 +/- √[54^2 - 4(144)])/2
x = (54 +/- √2340)/2
x = (54 +/- 2√585)/2
x = 27 +/- √585
x = 51.1867, 2.8132