MAT 1234 Calculus I Section 3 2 The

MAT 1234 Calculus I Section 3. 2 The Mean Value Theorem http: //myhome. spu. edu/lauw

Quiz, HW, and … l l l HW 3. 2 Please prepare for the next exam. Review problems from your past HW. Make sure you can do all the problems without any help.

10/30 Friday l l l Last day to withdraw from a class. Talk to me (or your advisor) if you have any questions. I and your advisor are here to help you make an informed decision.

Preview l We are going to take a look at some theoretical background materials • Rolle’s Theorem • The Mean Value Theorem • Consequences of the Mean Value Theorem

We know this, right? l

Recall: Definition l

Recall: Geometric Meaning l 0 2 2

In Other Words… l 0 2 2

In Particular… l

Preview l l l Rolle’s Theorem The Mean Value Theorem Consequences of the Mean Value Theorem We are going to convince ourselves that these results are correct. Sometimes, a diagram is sufficient. Other times, we need more details.

Rolle’s Theorem l

Recall and Translation l

Rolle’s Theorem

Rolle’s Theorem

Example 1* Show that real root. has exactly one

Example 1* (Q&A) Why do we need to show it when it is obvious from the graph?

We know… l

T or F l

T or F l

The Mean Value Theorem l

The Mean Value Theorem

The Mean Value Theorem

Example 2 l

Sage. Math Illustration l http: //myhome. spu. edu/lauw/Sage/MVT. html

Theorem (Consequence of the MVT) l

Why? (1) l

Why? (2) l

Why? (3) l

Why? (4) l

Where Are We Going to Use This? l 5. 3 Antiderivatives

Corollary (Important)

Corollary (Important) Why?

Wai? (1)

Wai? (2)

Wai? (3)

Possible Exam Questions l l l State the Rolle’s Theorem State the Mean Value Theorem Explain why the following is true

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