Download presentation

Presentation is loading. Please wait.

1
**Rolle’s Theorem and The Mean Value Theorem**

4.2

2
**If f (x) is a differentiable function over [a,b], then at some point between a and b:**

Mean Value Theorem for Derivatives

3
**If f (x) is a differentiable function over [a,b], then at some point between a and b:**

Mean Value Theorem for Derivatives Differentiable implies that the function is also continuous.

4
**If f (x) is a differentiable function over [a,b], then at some point between a and b:**

Mean Value Theorem for Derivatives Differentiable implies that the function is also continuous. The Mean Value Theorem only applies over a closed interval.

5
**If f (x) is a differentiable function over [a,b], then at some point between a and b:**

Mean Value Theorem for Derivatives The Mean Value Theorem says that at some point in the closed interval, the actual slope (instantaneous rate of change) equals the average slope (average rate of change).

6
**Tangent parallel to chord.**

Slope of tangent: Slope of chord:

7
**To find c, set derivative = to 4**

Example Suppose you have a function f(x) = x^2 in the interval [1, 3]. To find c, set derivative = to 4

8
**There can be more than 1 value of c that satisfy MVTD**

9
**There is no value of c that satisfies this equation. Why?**

f(x) is not continuous in the given interval!

12
**Since f(0) = f(12), Rolle’s Theorem applies**

Find the value of c that satisfies the MVTD: Since f(0) = f(12), Rolle’s Theorem applies

13
**Since f(0) = f(1), Rolle’s Theorem applies**

Find the value of c that satisfies the MVTD: Since f(0) = f(1), Rolle’s Theorem applies

14
Example A trucker handed in a ticket at a toll booth showing that in 2 hours she had covered 159 miles on a toll road with a speed limit of 65 mph. Can the trucker be cited for speeding? MVTD tells us at some point in the interval, the instantaneous velocity is equal to the average velocity! Thus she must have been speeding at some point! Average velocity is 159/2 = 79.5

Similar presentations

OK

Mean Value Theorem for Derivatives4.2 Teddy Roosevelt National Park, North Dakota Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie.

Mean Value Theorem for Derivatives4.2 Teddy Roosevelt National Park, North Dakota Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on fibonacci numbers in music Ppt on cross docking pictures Ppt on food security in india Ppt on short story writing Ppt on dances of india Ppt on school management system Convert pdf to ppt online adobe Ppt on network theory concepts Ppt on cell the fundamental unit of life Ppt on iso-22000 and haccp