Question 23 If f(x) = 4x² - f(4.3)~ < > 7x + 5, find f'(4). Use this to find the linear approximation to f(x) at x = 4. The equation of this linear approximation is L(x) = Use L(x) to approximate f(4.3). (Compute the actual value of L(4.3).) Compare this with the actual value of f(4.3): =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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Question 23
<
f(4.3)~
>
If f(x) = 4x² 7x + 5, find f'(4).
Use this to find the linear approximation to f(x) at x = 4.
The equation of this linear approximation is
L(x) =
Use L(x) to approximate f(4.3). (Compute the actual value of L(4.3).)
Compare this with the actual value of f(4.3):
=
Transcribed Image Text:Question 23 < f(4.3)~ > If f(x) = 4x² 7x + 5, find f'(4). Use this to find the linear approximation to f(x) at x = 4. The equation of this linear approximation is L(x) = Use L(x) to approximate f(4.3). (Compute the actual value of L(4.3).) Compare this with the actual value of f(4.3): =
Question 24
< >
Use linear approximation, i.e. the tangent line, to approximate √81.2 as follows:
Let f(x)=√x. Find the equation of the tangent line to f(x) at x = 81
L(x) =
Using this, we find our approximation for V
/81.2 is
NOTE: For this part, give your answer to at least 9 significant figures or use an expression to give the exact
answer.
Transcribed Image Text:Question 24 < > Use linear approximation, i.e. the tangent line, to approximate √81.2 as follows: Let f(x)=√x. Find the equation of the tangent line to f(x) at x = 81 L(x) = Using this, we find our approximation for V /81.2 is NOTE: For this part, give your answer to at least 9 significant figures or use an expression to give the exact answer.
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