The Case of the Swiveling Spotlight

Patrick Sullivan Hannah Yan

The Problem:

• The police claim that they had the spotlight trained on the defendant’s car for more than 20 seconds. We need to prove that that is impossible using the power of CALCULUS!

What’s Happening?

How to prove the defendant is innocent

1. Find the slope of the spotlight line when it stops2. Create a third-degree polynomial by using integrals. 3. Find the roots of the third degree polynomial and

prove them using the intermediate value theorem4. Use Newton’s Method to find the accurate roots

and prove that the time must be less than 205. Prove the defendant innocent by using generated

constants. Explain why any constant will produce an innocent verdict.

Finding the Slope of the spotlight line when it stops

Creating a Third-Degree Polynomial

Proving Roots using the Intermediate Value Theorem

Proving that the root is less than 20 using generated constants

Proving roots using Newton’s Method

Proving to the Judge that the Suspect is INNOCENT