Example of a continuous function

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Homework Help Overview

The discussion revolves around identifying an example of a continuous function defined on a closed interval that does not have local maxima or minima at its endpoints. The focus is on graphical representation of such functions.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the requirements for a function to meet the criteria of having no local extrema at the endpoints, with suggestions to explore graphical representations and similar functions.

Discussion Status

The conversation is ongoing, with participants exploring the implications of the problem's requirements. Some guidance has been offered regarding the graphical approach, though there is uncertainty about its effectiveness.

Contextual Notes

The problem is constrained to graphical solutions, which raises questions about the utility of drawing graphs in this context.

joxer06
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Hi, just a home work question I am having problems with. it has to be solved graphically.

(1) Give an example of a continuous function f : [a,b] -> R that has no local maximum or local minimum at an endpoint
 
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There's not much one can do without basically giving you an answer. But you might try drawing some graphs that satisfy the requirements, then see if you can think of a function that's similar looking.
 
So neither endpoint is a local min or max, which means?
 
Last edited:
Oh, it has to be solved graphically. I guess drawing graphs wouldn't be so useful there. Sorry about that.
 

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