Suppose that f is a differentiable function with derivative

Question

𝑓'(𝑥) = (𝑥 − 3)(𝑥 + 1)(𝑥 + 5). Determine the intervals of x for which the function of f is increasing and decreasing.

Answer 1

since f'(x) =0 at x = -5, -1, 3 f' changes sign there.
Since f'(-6) < 0,
f is increasing (f' > 0) in (-5,-1) and (3,∞)
f is decreasing on (-∞,-5) and (-1,3)

This is just Algebra II. Recall what you know about the properties of polynomials.