September 23 - Proof by contradiction and MVT

As we learned yesterday, the Mean Value Theorem is essentially Rolle's Theorem generalized so the two points (a,b) do not have to output the same y-value. We did not have a quiz today, but we will on Monday involving the Mean Value Theorem in an "interesting" way. Last night's homework applied the MVT to finding the c value guaranteed by the theorem and to a proof (p.176 #79). This proof, however, involved more algebra than it did calculus.

In class yesterday, we were first introduced to Proof by Contradiction with an example. This method of proof requires that in order to prove a statement, you must show that everything besides that statement is not possible. The difficulty in these type proofs is determining how to approach it and making a supposition to disprove.

Today in class we worked another example of a Proof by Contradiction. The homework tonight includes 3 such proofs.

Notes from today are below.