Question

Find the critical numbers of the function f(x) = x^3 - 3x^2 - 9x + 30. x =

Answer 1

The critical numbers of the function f(x) = x^3 - 3x^2 - 9x + 30 are x = 3 and x = -1.

Step-by-step explanation:

Solution:

1. To find the critical numbers of the function f(x) = x^3 - 3x^2 - 9x + 30, we need to determine the values of x where the derivative of the function is equal to zero or undefined.
2. First, we find the derivative of f(x): f'(x) = 3x^2 - 6x - 9.
3. Next, we set f'(x) equal to zero and solve for x: 3x^2 - 6x - 9 = 0.
4. we can factor this equation as (x - 3)(x + 1) = 0 and solve for x to get: x = 3 or x = -1.
5. So, the critical numbers of the function f(x) = x^3 - 3x^2 - 9x + 30 are x = 3 and x = -1.