A function that is continuous over a finite closed interval necessarily have both a maximum and a minimum value over that interval.

True or False

Question

A function that is continuous over a finite closed interval necessarily have both a maximum and a minimum value over that interval.

True or False

jdoe0001 · Answer

let's take a peek at one|dw:1374353663432:dw|

jdoe0001 · Answer

what do you think?

anonymous · Answer

so is it true?

jdoe0001 · Answer

well, do you see a maximum? what about a minimum?

jdoe0001 · Answer

http://www.mathsisfun.com/algebra/images/function-max-min.gif

jdoe0001 · Answer

as you can see in the picture, a maximum is a "hump" in the graph
a minimum is a "burrow"

anonymous · Answer

so it's false? unless 5 and -5 are considered the maximum and minimum on there?

jdoe0001 · Answer

well, 5 and -5 would be considered maximum and minimum in the number interval context, yes,  you're correct

but what's being asked is in the function's graph context, so is false
as you can see a horizontal line function is continuous yet it has neither

anonymous · Answer

Alright. I get it now. thank you

jdoe0001 · Answer

yw

anonymous · Answer

Just to be sure it's false right? lol I like clarity

jdoe0001 · Answer

yes is $\bf \huge \sf \color{red}{false}$