Ellie has 200 dollars in her wallet at 10:00 AM when she goes to the mall. Afterwards, at 4 PM she has only 5 dollars left.
Is it possible that Ellie had exactly 100 dollars at one point?
Explain.
My guess to this question would be yes and I would use the Intermediate Value Theorem to back up my claim.
It is certainly possible, but by no means necessary.
The IVT only applies to continuous functions, and money comes in discrete steps.
Ellie might have gone from having $102.37 to only having $93.18, depending on what she bought.
Or, she might have spent $195 on one item, and gone right from 200 to 5 in one leap.