Question

The derivative of a function is f'(x)=x(x+2)(x-5). Find the value of x at each point where f has a
(a) local maximum,
(b) local minimum, or
(c) point of inflection

Answer 1

there are max/min at x = -2, 0, 5

f''(x) = 3x^2 - 6x - 10
at -2, 0, -5, f'' = 14, -10, 95

so, min at x = -2
max at x = 0
min at x = 5

inflection at 1±√39/3