View by Category

The presentation will start after a short

(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!

(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 – The Derivative PowerPoint presentation | free to view - id: 21aa92-ZGQwM

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

The Derivative

- The Definition of the DerivativeSlope of the

Tangent LineDerivative and DifferentiabilityDeri

vatives GraphicallyDifferentiability and

ContinuityDerivatives as Functions

The Definition of the Derivative

Definition

The Definition of the Derivative

Definition

Notations

Recall that by previous considerations, the

derivative of a function f at the point x0 is

the slope of the tangent line of the graph of f

at the point (x0,f(x0)). This is an important

geometric view to the derivative.

Slope of the Tangent Line (1)

To compute the equation of the tangent line, at a

point (a,f(a)) of the graph of a function f

observe that

Slope of the Tangent Line (2)

Example

Slope of the Tangent Line (2)

Example

Solution

Slope of the Tangent Line (2)

Example

Solution

Slope of the Tangent Line (2)

Example

Solution

Slope of the Tangent Line (2)

Example

Solution

Slope of the Tangent Line (3)

Example

Solution (contd)

Conclusion

Derivative and Differentiability (1)

Definition 1

Derivative and Differentiability (1)

Definition 1

Definition 2

Derivative and Differentiability (1)

Definition 1

Definition 2

Derivative and Differentiability (2)

Theorem

Derivative and Differentiability (2)

Theorem

Proof

?

Derivative and Differentiability (3)

Theorem

Proof (contd)

?

Differentiability Graphically

Differentiability Graphically

Differentiability Graphically

Differentiability Graphically

Differentiability and Continuity

Theorem

Proof

The Derivative as a Function

Definition

Notation

The derivative of a function f is a function

whose the domain of definition consists of all

the numbers x such that the function f has

its derivative at the point x.

Graphs of Functions and their Derivatives

Problem

The picture on the right shows the graphs of two

functions f and g and the graphs of their

derivatives. The maximum of the shown values of

f is larger than that of g. Which is which?

Graphs of Functions and their Derivatives

Df

Problem

f

The picture on the right shows the graphs of two

functions f and g and the graphs of their

derivatives. The maximum of the shown values of

f is larger than that of g. Which is which?

Solution

The red curve appears to intersect the x-axis

whenever the tangent of the blue curve is

horizontal. Hence the red curve is the graph of

the derivative of the function f. The blue

curve is the graph of f.

g

Dg

The green curve is everywhere decreasing. Hence

its tangents have negative slopes. The black

curve is the only curve that takes only negative

values. Hence the green curve is the graph of

the function g and the black curve that of its

derivative.

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

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!

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: "The Derivative" 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!