Consider the function f(x) = . - sin(x) + 1. 2 (a) Approximate the relative extrema of f. (Enter your answers as a comma-separated list. Round your answers to four decimal places.) X = (b) Find the tangent line approximation of f at- TL 2 (c) Use your tangent line approximation to approximate the value of f(1.9). (Round your answer to three decimal places.) Is your approximation an underestimate or an overestimate of the actual value of f(1.9)? O underestimate O overestimate
Consider the function f(x) = . - sin(x) + 1. 2 (a) Approximate the relative extrema of f. (Enter your answers as a comma-separated list. Round your answers to four decimal places.) X = (b) Find the tangent line approximation of f at- TL 2 (c) Use your tangent line approximation to approximate the value of f(1.9). (Round your answer to three decimal places.) Is your approximation an underestimate or an overestimate of the actual value of f(1.9)? O underestimate O overestimate
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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![Consider the function \( f(x) = \frac{x^3}{2} - \sin(x) + 1 \).
(a) Approximate the relative extrema of \( f \). (Enter your answers as a comma-separated list. Round your answers to four decimal places.)
\[ x = \underline{\hspace{2cm}} \]
(b) Find the tangent line approximation of \( f \) at \( \frac{\pi}{2} \).
\[ \underline{\hspace{4cm}} \]
(c) Use your tangent line approximation to approximate the value of \( f(1.9) \). (Round your answer to three decimal places.)
\[ \underline{\hspace{4cm}} \]
Is your approximation an underestimate or an overestimate of the actual value of \( f(1.9) \)?
- \( \bigcirc \) underestimate
- \( \bigcirc \) overestimate](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F466923f0-6f55-4935-bc1a-e5c184127f99%2Fe444299f-b821-4d4a-b7e2-c5853ebf10e4%2Faardjef_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the function \( f(x) = \frac{x^3}{2} - \sin(x) + 1 \).
(a) Approximate the relative extrema of \( f \). (Enter your answers as a comma-separated list. Round your answers to four decimal places.)
\[ x = \underline{\hspace{2cm}} \]
(b) Find the tangent line approximation of \( f \) at \( \frac{\pi}{2} \).
\[ \underline{\hspace{4cm}} \]
(c) Use your tangent line approximation to approximate the value of \( f(1.9) \). (Round your answer to three decimal places.)
\[ \underline{\hspace{4cm}} \]
Is your approximation an underestimate or an overestimate of the actual value of \( f(1.9) \)?
- \( \bigcirc \) underestimate
- \( \bigcirc \) overestimate
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