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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 e

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 e

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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7. Find the exact x-value where the function f (x) = x + ln x 2 – 1) attains a maximum value. An estimated answer or a calculator answer will not e 8. Using the Mean Value Theorem and Rolle's Theorem, show that‡3 + 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 is concave up and concave down. Phy
Transcribed Image Text:7. Find the exact x-value where the function f (x) = x + ln x 2 – 1) attains a maximum value. An estimated answer or a calculator answer will not e 8. Using the Mean Value Theorem and Rolle's Theorem, show that‡3 + 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 is concave up and concave down. Phy
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