SECTION 3-2Rolle’s and Mean Value Theorem

Rolle’s Theorem

Let f be differentiable on (a,b) and continuous on [a,b]. If , then there is at least one point c belonging to (a,b) where 0)( cf

)()( bfaf

a b

0)( cf

c

1. Determine whether Rolle’s Theorem can be applied on the interval, then find the values of c in the interval given the function with an interval of [1,2]23)( 2 xxxf

2.) Determine whether Rolle’s Theorem can be applied on the interval, then find the values of c in the interval given the function with an interval of [-2,2]xxxf 32)( 3

1

3. Determine whether Rolle’s Theorem can be applied on the interval, then find the values of c in the interval given the function with an interval of [2,4]xxxf 23)( 2

Mean Value Theorem

• Let f be differentiable on (a,b) and continuous on [a,b], then there exists a point c belonging to (a,b) where

ab

afbfcf

)()()(

a bc

)(cf

ab

afbf

)()(

4.) Find the number which satisfies the MVT for the function on [-1,3]75)( 2 xxxf

5. Find the number which satisfies the MVT for the function on [1,2]3

6)(

xxf

6.) Find the number which satisfies the MVT for the function

on [0,])cos()2sin()( xxxf

7.) Suppose the police time you going from one mile to the next in 51.4 seconds. If you are traveling in a 55 mph zone, do you deserve a ticket?

trd

Homework

pg 176 # 2, 3, 11,12,14,15,18,20,23, 39,40, 42,43, 44, 46, and 47