Q. 7 - Calculus

Question

Suppose f is a function that is discontinuous somewhere on an interval I. Explain why comparing the values of any local extrema of f on I and the values or limits of f at the endpoints of I is not in general sufficient to determine the global extrema of f on I. 

Step-by-Step Solution

Answer

Comparing the values of any local extrema of f on I and the values or limit of f at the endpoints of I is not in general sufficient to determine the global extrema of f on I because f might have a vertical asymptote on I.

Step 1. Given information.

We have to explain that :  Suppose f is a function that is discontinuous somewhere on an interval I. Explain why comparing the values of any local extrema of f on I and the values or limits of f at the endpoints of I is not in general sufficient to determine the global extrema of f on I. 

Step 2. Explanation

Comparing the values of any local extrema of f on I and the values or limit of f at the endpoints of I is not in general sufficient to determine the global extrema of f on I because f might have a vertical asymptote on I.