Question

What are the critical points of the function f(x) = x³ - 12x - 5?

A. x = 2
B. x = -2
C. x = 0
D. x = 1
E. x = -1

Answer 1

The critical points of the function f(x) = x³ - 12x - 5 are found by setting the derivative f'(x) to zero, resulting in the points x = 2 and x = -2.

Step-by-step explanation:

The critical points of a function are found by taking the derivative of the function and setting it equal to zero. For the function f(x) = x³ - 12x - 5, we need to calculate f'(x) which gives us 3x² - 12. Setting the derivative equal to zero: 3x² - 12 = 0.

Now we solve for x:

1. Divide both sides by 3, we get x² = 4.
2. Take the square root of both sides, we get x = ±2.

Therefore, the critical points for the function f(x) = x³ - 12x - 5 are x = 2 and x = -2.