Question

Find all of the critical points of the function f(x)=|3x|.

A) x = 0
B) x = 3
C) x = -3, 3
D) x = -3

Answer 1

The critical points of the function f(x) = |3x| are x = -3 and x = 3.

Step-by-step explanation:

The function f(x) = |3x| has critical points at x = 0 and x = -3, 3. To find these critical points, we need to determine where the derivative of the function is equal to zero or undefined. For f(x) = |3x|, the derivative is f'(x) = 3 sign(x), where sign(x) is the sign (positive or negative) of x. The derivative is undefined at x = 0 and changes sign at x = -3, 3, indicating critical points at these values. Therefore, the correct answer is C) x = -3, 3.