Graphical Proof: The Max-Min Theorem Does Not Hold for Non-Continuous Functions

[joxer06]

Hi, just trying to do some homework for college and I can't get my head around this question. It is a question to show that if you take away the condition of a function being continuous, the max-min theorem no longer holds true. Any help is greatly appreciated!

Suppose that f: [a,b] -> R is not continuous. Show that f need not have an absolute maximum and an absolute minimum on [a,b]. (Answer in graphical form)

 

[Dick]

Tell me about f(x)=1/(x-a) if x not equal to a and f(x)=0 if x=a. Then graph it.