warmup

Be seated before the bell rings

DESK

homeworkWarm-up (in your notes)

Agenda : go over hwHw quiz

Notes lesson 3.2

NotebookTable of content

Page1

Learning Target 1

13) Extreme Values

14) Role’s ThmMVT

LT2: State and use Rolle’s and Mean Value Theorem

HW: p.174; 1-4,9-11,27,31-34,37-43odd ,51

3.2 Role’s Theorem

An extreme value must occur if certain things happen in the graph.

If __________________then ________________.

Review: IVT?Continuous. Y-value is in the middle

There exist a c such that f(c) = y.

3.2 Role’s Theorem

An extreme value must occur if certain things happen in the graph.

If __________________then ________________.

If f is continuous from [a, b], f Is differentiable from (a , b) and f(a) = f(b) Then there is at least one “c” value s.t f’(c) = 0.

Does Role’s Theorem apply? 1( )3

f xx

4,01) No, b/c not cont. & diff

( ) 1f x x 1,32) No, b/c (1) (3)f f( ) ( )f a f b

4 2( ) 2f x x x 2,23) yes, Cont. Diff.

( 2)f

( ) ( )f a f b

(2)f

8

8

Find the c-value 4 2( ) 2f x x x 2,23)

yes, Cont. Diff.

( 2)f

( ) ( )f a f b

(2)f

8

8

Then there is at least one “c” value s.t f’(c) = 0.

30 4 4x x 20 4 ( 1)x x

0 4 ( 1)( 1)x x x 0, 1, 1x x x

Role’s Theorem: Rolling down the Hill

Mean Value theorem: If f is continuous [a,b] and differential (a,b),Then

a b

( ) ( )f b f ab a

'( )f c

Instantaneous ROC = average ROC

Steps#1 -

( ) ( )f b f ab a

#2 -

'( )f c #3 -

45yx

Ex: 1,4

Decide if MVT can be apply. If so find the c guarantee by the MVT.