The Case of the Swiveling Spotlight
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Transcript of The Case of the Swiveling Spotlight
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