Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Use linear approximation to estimate $f(5.1)$ given that $f(5)=10$ and $f^{\prime}(5)=-2$

$\quad L(x)=-2 x+20$ and $f(5.1)=L(5.1)=9.8$

Calculus 1 / AB

Chapter 4

Applications of the Derivative

Section 6

Linear Approximation and Differentials

Derivatives

Differentiation

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

04:40

In mathematics, a derivati…

44:57

In mathematics, a differen…

00:45

Linear approximation Estim…

03:20

Given that $ f $ is a diff…

03:22

Suppose $f$ is differentia…

02:12

Use linear approximation t…

01:42

Suppose $f(1,2)=4, f_{x}(1…

00:51

01:02

Use a linear approximation…

01:08

Given that $f$ is a differ…

02:48

Linear approximation Find …

03:49

Using a Tangent Line Appro…

05:59

00:25

Evaluate a function.Gi…

08:29

00:40

Use each graph to estimate…

00:27

Use a calculator to estima…

02:34

Linear approximationa.…

02:20

00:47

04:10

Use the given graphs of $ …

04:21

in this problem, we need to take our linear approximation formula substituted known values to get our linear approximation equation for this set up and then a substitute in 5.1 into this equation to get our answer of fo 5.1. So let's start by substituting in our known values in this case, A is going to equal five because that is the given value. We haven't that is given value for this problem. So our Ella Vex is going to be F five plus of prime of five times ex my size now each effort five and a terrified of we know what those are 10 and negative two, respectively. So we can rewrite this as l've X equals 10 minus two times X minus five, I wrote minus students that have plus negative, too, because the negative just carries over the positive. So it's really just 10 minus two times X minus five and simplifying this down. We get our final at l A X equation, which is negative two X plus 20. So this is our final of X, and what we can now do have solved for F of 5.1 is Since this is the linear approximation at f of five, we can substitute 5.1 and for X and get our final answer. So L a five point warned equals F of 5.1, which equals negative two times 5.1, uh, plus 20. And this equals 9.8, which is our final answer.

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, a derivative is a measure of how a function changes as its i…

In mathematics, a differentiation rule is a rule for computing the derivativ…

Linear approximation Estimate $f(5.1)$ given that $f(5)=10$ and $f^{\prime}(…

Given that $ f $ is a differentiable function with $ f(2, 5) = 6 $, $ f_x(2,…

Suppose $f$ is differentiable on $(-\infty, \infty)$ and $f(5.01)-f(5)=0.25 …

Use linear approximation to estimate $f(3.85)$ given that $f(4)=3$ and $f^{\…

Suppose $f(1,2)=4, f_{x}(1,2)=5,$ and $f_{y}(1,2)=-3$Find the linear app…

Linear approximation Estimate $f(3.85)$ given that $f(4)=3$ and $f^{\prime}(…

Use a linear approximation to estimate the given number.$(2.001)^{5}$

Given that $f$ is a differentiable function with $f(2,5)=6$ ,$f_{x}(2,5)…

Linear approximation Find the linear approximation to the following function…

Using a Tangent Line Approximation In Exercises $5-10$ , find the tangent li…

Evaluate a function.Given $f(x)=5 x+1,$ find $f(2)$.

Use each graph to estimate the values of $x$ for which $f(x)=5 .$ Then write…

Use a calculator to estimate $f^{\prime}(a)$ for the given value of $a$.…

Linear approximationa. Find the linear approximation to the function $f$…

Use the given graphs of $ f $ and $ g $ to estimate the value of $ f (g(x)) …

01:26

Sketch a graph of a function $f$ with the following properties.$$\begin{…

00:58

How can linear approximation be used to approximate the change in $y=f(x)$ g…

02:36

Estimating speed Use the linear approximation given in Example 1 to answer t…

02:06

Derivatives of logarithmic functions Calculate the derivative of the follow…

02:49

Find the following limits or state that they do not exist. Assume $a, b, c,$…

02:13

Calculating limits exactly Use the definition of the derivative to evaluate…

02:52

Linear approximationa. Write the equation of the line that represents th…

00:13

Give examples of each of the following.a. A limit with the indeterminate…

02:27

Logarithmic differentiation Use logarithmic differentiation to evaluate $f…