Download presentation

Presentation is loading. Please wait.

Published byDante Holbrooks Modified over 2 years ago

1
2.4 Rates of Change and Tangent Lines Devil’s Tower, Wyoming Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1993

2
The slope of a line is given by: The slope at (1,1) can be approximated by the slope of the secant through (4,16). We could get a better approximation if we move the point closer to (1,1). ie: (3,9) Even better would be the point (2,4).

3
The slope of a line is given by: If we got really close to (1,1), say (1.1,1.21), the approximation would get better still How far can we go?

4
slope slope at The slope of the curve at the point is:

5
is called the difference quotient of f at a. If you are asked to find the slope using the definition or using the difference quotient, this is the technique you will use.

6
In the previous example, the tangent line could be found using. The slope of a curve at a point is the same as the slope of the tangent line at that point. If you want the normal line, use the negative reciprocal of the slope. (in this case, ) (The normal line is perpendicular.)

7
Example 4: a Find the slope at. Let On the TI-89: limit ((1/(a + h) – 1/ a) / h, h, 0) F3Calc Note: If it says “Find the limit” on a test, you must show your work!

8
Example 4: b Where is the slope ? Let On the TI-89: Y= y = 1 / x WINDOW GRAPH

9
Example 4: b Where is the slope ? Let On the TI-89: Y= y = 1 / x WINDOW GRAPH We can let the calculator plot the tangent: F5Math A: Tangent ENTER 2 Repeat for x = -2 tangent equation

10
Review: average slope: slope at a point: average velocity: instantaneous velocity: If is the position function: These are often mixed up by Calculus students! So are these! velocity = slope

Similar presentations

OK

Colorado National Monument Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003 AP Calculus AB/BC 3.3 Differentiation Rules,

Colorado National Monument Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003 AP Calculus AB/BC 3.3 Differentiation Rules,

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Natural disasters for kids ppt on batteries Ppt on regional rural banks in india Free ppt on smart note taker ppt Ppt on team building training Ppt on operating system basics Ppt on blue eyes technology free download Ppt on acid-base titration formula Ppt on hindi grammar for class 9 Ppt on church leadership Ppt on power sharing in india