Q. 4 - Calculus

Question

Explain why you can’t find the global maximum of a function f on an interval I just by finding all the local extrema of f and then checking to see which one has the highest value f(c) 

Step-by-Step Solution

Answer

The critical points of the function f 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 why we can’t find the global maximum of a function f on an interval I just by finding all the local extrema of f and then checking to see which one has the highest value f(c) 

Step 2. Explanation

The critical points of the function f 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.