Question

Given the function f(x) = -1/3(x³) - 9(x²), find all x-values where f has an inflection point.

A) x = -9/2
B) x = 0
C) x = 3
D) The function has no inflection point.

Answer 1

The function has an inflection point at x = -9/2.

Step-by-step explanation:

To find the x-values where the function has inflection points, we need to find the second derivative of the function and find where it equals zero. The second derivative of f(x) = -1/3(x³) - 9(x²) is f''(x) = -2x - 18x. Setting f''(x) = 0, we get -2x - 18 = 0. Solving for x, we find x = -9/2. Therefore, the correct option is A) x = -9/2.