Once Upon a Time...

Captain Integration was cruising down the interstate, making his weekly trip from Head Quarters to the Children's Hospital...

This particular morning, however, Captain Integration was running awfully late for his 9 AM appointment for reading to the sick children of the hospital.

The hospital was approximately 80 miles from HQ with the speed limit being 55 mph all the way there. Captain Integration left at 8 am, passing through a toll booth, and arrived at 9 am passing through another toll booth.

Captain Integration was Speeding!

Speed Limit:55

Little did Captain Integration know, a nearby police officer, Cal, was observing his reckless driving.

Since Captain Integration's car was faster than fast, Cal knew that there was no way that he could ever pull him over.

So, the officer had devised a plan to catch Captain Integration in a mathematical speed trap!

!

Cal kept track of the times that Captain Integration passed through the toll booths.

All in all, the officer gathered that Captain had managed to go 80 miles in exactly one hour- all the while when he was in a 55 mph speed zone.

Cal the Cop had all the data he needed to use the Mean Value Theorem and prove that Captain Integration was driving way too fast.

Mean Value Theorem: