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4. Find the Linearization of f(x) = sinx at a = . Provide your answer as L(x) =? 5. Use Linear Approximation to estimate e(-0.01). Provide your answer in 2 decimal places. Do not use a calculator. Show work for credit. 6. Calculate the locations of maximums and minimums of the following functions: Show work in details. f(x) = x³ 3x + 2 • f(x)=x¹8x² +3

4. Find the Linearization of f(x) = sinx at a = . Provide your answer as L(x) =? 5. Use Linear Approximation to estimate e(-0.01). Provide your answer in 2 decimal places. Do not use a calculator. Show work for credit. 6. Calculate the locations of maximums and minimums of the following functions: Show work in details. f(x) = x³ 3x + 2 • f(x)=x¹8x² +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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Solve 4,5&6
4. Find the Linearization of f(x) = sinx at a = . Provide your answer as L(x) =? 5. Use Linear Approximation to estimate e(-0.01). Provide your answer in 2 decimal places. Do not use a calculator. Show work for credit. 6. Calculate the locations of maximums and minimums of the following functions: Show work in details. • f(x) = x³ - 3x + 2 • f(x)=x²-8² +3 7. Find the exact x-value where the function f(x) = x + ln (x² - 1) attains a maximum value. An estimated answer or a calculator answer will not earn any credit. 8. Using the Mean Value Theorem and Rolle's Theorem, show that³+x-1=0) has exactly one real root. 9. If f(1) = 10 and f'(x) ≥ 2 for 1 ≤ x ≤ 4, how small canf (4) possibly be? 10. The graph of a function is given below. Determine the intervals on which the function i concave up and concave down. you
Transcribed Image Text:4. Find the Linearization of f(x) = sinx at a = . Provide your answer as L(x) =? 5. Use Linear Approximation to estimate e(-0.01). Provide your answer in 2 decimal places. Do not use a calculator. Show work for credit. 6. Calculate the locations of maximums and minimums of the following functions: Show work in details. • f(x) = x³ - 3x + 2 • f(x)=x²-8² +3 7. Find the exact x-value where the function f(x) = x + ln (x² - 1) attains a maximum value. An estimated answer or a calculator answer will not earn any credit. 8. Using the Mean Value Theorem and Rolle's Theorem, show that³+x-1=0) has exactly one real root. 9. If f(1) = 10 and f'(x) ≥ 2 for 1 ≤ x ≤ 4, how small canf (4) possibly be? 10. The graph of a function is given below. Determine the intervals on which the function i concave up and concave down. you
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