View by Category

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

Loading...

PPT – Calculus I PowerPoint presentation | free to view - id: 1d318b-MGE3N

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Calculus I

- Section 2.7 Derivatives and Rates of Change

Section 2.7 Derivatives and Rates of Change

- Def Let f be a function that is continuous on

a small neighborhood of a point P on the graph of

f, P(a, f(a)). Then to determine the slope of the

tangent line to the graph of f at P, we start by

considering a point Q(x, f(x)) close to P, with x

? a. Then the slope of the secant line through

PQ

Section 2.7 Derivatives and Rates of Change

f

.

Q(x, f(x))

Then the tangent line to the curve of y f(x)

at the point P(a, f(a)) is the line through P

with slope provided the limit exists.

.

P(a, f(a))

Section 2.7 Derivatives and Rates of Change

- Example 1
- Use the above definition to find an equation

of the tangent line to the graph of - f(x) 3x2- 2x 1 at the point P(2, 9).

Section 2.7 Derivatives and Rates of Change

- Example 2
- Use the above definition to find an equation

of the tangent line to the graph of - f(x) vx at the point P(16, 4).

Section 2.7 Derivatives and Rates of Change

f

.

Q(ah, f(ah))

Then the tangent line to the curve of y f(x)

at the point P(a, f(a)) is the line through P

with slope provided the limit exists.

.

P(a, f(a))

Section 2.7 Derivatives and Rates of Change

- Example 3
- Use the above definition to find an equation

of the tangent line to the graph of - f(x) at the point P(1, 3).

Section 2.7 Derivatives and Rates of Change

- Def The derivative of a function f at a number

a, denoted by f(a) is - If this limit exists.
- So, f(a) is the slope of the tangent line at x

a, - the instanteneous rate of change of f at x a.

Section 2.7 Derivatives and Rates of Change

- Example 4
- Use the above definition to find f(a)
- f(x)

Section 2.7 Derivatives and Rates of Change

- Example 5
- If a rock is thrown into the air with a

velocity of 40 ft/s, its height (in feet) after t

seconds is given by y 40t 16t2. Find the

velocity when t 2. - RECALL Average Velocity
- Instantaneous Velocity v(a) f(a)
- Where f is the position function.

Section 2.7 Derivatives and Rates of Change

- Reference
- Stewart, Single Variable Calculus
- Early Transcendentals

About PowerShow.com

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Page of

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2016 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2016 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Calculus I" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!

Committed to assisting Saintleo University and other schools with their online training by sharing educational presentations for free