Question

To find where the function is increasing and decreasing, which function do we plug the critical points into?

a) f'(x)
b) f''(x)
c) f(x)
d) None of the above

Answer 1

To determine where a function is increasing or decreasing, you should plug the critical points into its first derivative, f'(x).

Step-by-step explanation:

To find where the function is increasing and decreasing, we plug the critical points into the derivative of the function, f'(x). If f'(x) > 0 at a critical point, the function is increasing at that interval. Conversely, if f'(x) < 0, the function is decreasing. Critical points give us potential locations where the behavior of the function may change, but we check those points using the first derivative to know the function's increasing or decreasing behavior. The second derivative, f''(x), is used to determine concavity and points of inflection, not whether the function is increasing or decreasing. Therefore, the correct answer is a) f'(x).