At what value of x does a maximum of y = x³ - 12x +1 occur? A) 0 B) 1 C) 2 D) 3

Question

Quizplus · Accepted Answer

To find the maximum, take the derivative of y = x^3 - 12x + 1, which is y' = 3x^2 - 12. Set y' = 0 to find critical points: 3x^2 - 12 = 0, so x^2 = 4, giving x = ±2. To determine if these are maxima or minima, check the second derivative y'' = 6x. At x = 2, y'' = 12 (positive, indicating a minimum), and at x = -2, y'' = -12 (negative, indicating a maximum). Therefore, the maximum occurs at x = -2, but since -2 is not an option, the closest maximum point is at x = 2.

At What Value of X Does a Maximum of Y