Download presentation

Presentation is loading. Please wait.

Published byClarissa claudia Garcia Modified over 2 years ago

1
Local Linearization (Tangent Line at a point)

2
When the derivative of a function y=f(x) at a point x=a exists, it guarantees the existence of the tangent line at that point. Nearby the point of tangency, the graph of f(x) looks like the tangent line at the point (a, f(a)). This result is expressed by saying that nearby x=a, the values of f(x) are approximately the same as the values of the tangent line at x=a, or that 2

3
Graphs of f(x) and Its Tangent Line nearby x=2 In the following slides look at the difference between the values of f(x) and the values of the tangent line at x=2 for values of x “close” to 2 3

4
What is the largest distance between the function and its tangent line? __________ What is the largest error made if the tangent line is used to estimate values of the function? _______ The estimates using the tangent line are under or overestimate? _____________ How do you know? 4

5
What is the largest error made if the tangent line is used to estimate values of the function? _______ 5

6
6

7
What happens with the error made if the tangent line is used to estimate values of the function? 7

8
Estimating Values Using the Tangent Line Use linearization of y=x 2 to estimate o 3.3 2 o 2.5 2 o 4.7 2 8

9
9 For 3.3 2 use the the tangent line at the point (3,9) Equation of tangent line at (3,9) is _____________________ Estimate the value of the tangent line at x=3.3 Is it an overestimate/underestimate? Use the sign of y”(3) to determine whether the tangent line is above or below y=x 2 nearby x=3 Do the other estimates

10
Exercise Estimate the value of 2.8 3 using linear approximations Choose a function to work (from the basic ones) Choose the point at which you want to find the tangent line line (easy to work with) Find the linearization of the function at that point and use it to estimate your answer Is your answer an over/underestimate? 10

Similar presentations

OK

7 = 7 SOLUTION EXAMPLE 1 Check the intersection point Use the graph to solve the system. Then check your solution algebraically. x + 2y = 7 Equation 1.

7 = 7 SOLUTION EXAMPLE 1 Check the intersection point Use the graph to solve the system. Then check your solution algebraically. x + 2y = 7 Equation 1.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on union parliament of india Ppt on conservation of mass Ppt on revolution of the earth and seasons solar Ppt on credit policy pdf Ppt on polynomials for class 8th Ppt on conservation of resources Ppt on sectors of indian economy class 10 Ppt on artificial intelligence in power system Ppt on first conditional pdf Ppt on any social issues in india