Question

Given f '(x) = (x − 4)(6 − 2x), find the x-coordinate for the relative minimum on the graph of f(x).

Answer 1

x = 3

Explanation:

f'(x) = 0 for x = 3 and x = 4 . . . . by the zero product rule.

The coefficient of x² in f'(x) is negative, so the parabola opens downward.

f''(x) is positive for x < 3.5, so the coordinate x = 3 represents a relative minimum.