maxima and minima. Use this information to sketch the curve. SOLUTION If f(x) = 3x - 24x³, then f'(x) = 12x - 72x² = 12x2(x - 6) f"(x) = 36x2 - 144x = 36x(x – 4). 6 To find the critical numbers we set f'(x) = 0 and obtain x = 0 and x = To use the Second Derivative Test we evaluate f" at these critical numbers: f"(0) = Video Example ) f"(6) = Since f'(6) = and f"(6) > 0, f(6) = is a local minimum. Since f"(0) = the Second Derivative Test gives no information about the critical number 0. But since f'(x) < 0 for x < 0 and also for 0