Let f(x)=(x-2)(x+3)^2. Find all the values c, such that f'(c)=0 in the interval [-3,2].

Question

Let f(x)=(x-2)(x+3)^2. Find all the values c, such that f'(c)=0 in the interval [-3,2].

Answer 1

f(x) = x³ - 4x² - 3x - 18

f'(x) = 3x - 8x - 3

f'(x) = (3x - 1)(x + 3)

Can you use zero product rule and answer?