Q. 3 - Calculus

Question

When you try to find the local extrema of a function f on an interval I, one of the first steps is to find the critical points of f . Explain why these critical points of f won’t help you locate any “endpoint” extrema. 

Step-by-Step Solution

Answer

The critical points of the function won't help to locate any endpoints extrema because the derivative of the function may or may not be zero or fails to exist at the endpoints of the interval. The critical point is always calculated by equating the first derivative of the function equal to zero.

Step 1. Given information.

We have to explain that when we try to find the local extrema of a function f on an interval I, one of the first steps is to find the critical points of f ,why these critical points of f won’t help us locate any “endpoint” extrema. 

Step 2. Explanation

The critical points of the function won't help to locate any endpoints extrema because the derivative of the function may or may not be zero or fails to exist at the endpoints of the interval. The critical point is always calculated by equating the first derivative of the function equal to zero.