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

Answer 1

let's take a peek at one

Answer 2

what do you think?

Answer 3

so is it true?

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

Alright. I get it now. thank you

Answer 10

yw

Answer 11

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

Answer 12

yes is \(\bf \huge \sf \color{red}{false}\)