Q. 5 - Calculus

Question

Suppose f is a function that is defined and continuous on an open interval I. Will the endpoints of I always be local extrema of f ? Will f necessarily have a global maximum or minimum in the interval I? Justify your answers.

Step-by-Step Solution

Answer

The endpoints of I always be local extrema off because there will not be any endpoint extrema.The function f may or may not be a global maximum (or minimum) on the interval

Step 1. Given information.

We have to explain that : Suppose f is a function that is defined and continuous on an open interval I. Will the endpoints of I always be local extrema of f ? Will f necessarily have a global maximum or minimum in the interval I? 

Step 2. Explanation

It is given that f is a function that is defined and continuous on an open interval I

The endpoints of I always be local extrema off because there will not be any endpoint extrema.

The function f may or may not be a global maximum (or minimum) on the interval