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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): =

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): =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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