11 3 the tangent line problem n.
Download
Skip this Video
Download Presentation
11.3 The Tangent Line Problem

Loading in 2 Seconds...

play fullscreen
1 / 19

11.3 The Tangent Line Problem - PowerPoint PPT Presentation


  • 167 Views
  • Uploaded on

11.3 The Tangent Line Problem. Spring 2011. At the end of this lesson, you should be able to. Use a tangent line to approximate the slope of a graph at a point. Use the limit definition of slope to find exact slopes of graphs.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about '11.3 The Tangent Line Problem' - indira-lancaster


Download Now An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
at the end of this lesson you should be able to
At the end of this lesson, you should be able to
  • Use a tangent line to approximate the slope of a graph at a point.
  • Use the limit definition of slope to find exact slopes of graphs.
  • Find derivatives of functions and use derivatives to find slopes of graphs.
tangent line to a graph page 7631
Tangent Line to a Graph (page 763)

The tangent line to a graph of a function f at a point is the line that …

To determine the rate at which a graph rises or falls at a single point, ….

slope of secant line
Slope of Secant Line

We can calculate the slope of a line given two points

y

Calculate the slope of the line between the given point P (5, 4) and another point on the curve, say Q(2, 1). The line is called a secant line.

P(5,4)

Q(2,1)

x

.

slide6

Slope and the Limit Process (page 765)

y

y=f(x)

( , )

( , )

x

0

________________

definition of a slope of a graph page 765
Definition of a Slope of a Graph (page 765)

The slope mof the graph of f(x) at the point (x, f(x))

is equal to the slope of its tangent line at (x, f(x)),

and is given by

provided this limit exists.

example 3 discussion
Example 3 (Discussion)

Why do you think the slope of is a constant number? Explain.

slide13
Example 4 (You try!) Find a formula for the slope of the graph of What are the slopes at points (-1,3) and (0,4)?
the derivative of a function page 768 769
The Derivative of a Function (page 768-769)

The derivative is the formula which gives the slope of the tangent line at any point x for f(x)

slide19

Practice

p.770-771 #s

1-45, every four