Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - Chapter 2 Review Exercises - Page 184: 22

Answer

a) 11.27 b) 0.48

Work Step by Step

a) $f(x) = x^{3}-x^{2}+1$ $f'(x) = 3x^{2}-2x$ $f'(x_{0}) = 3(x_{0})^{2} - 2(x_{0})$ As $x_{0} = 2.3$ $f'(2.3) = 3(2.3)^{2} - 2(2.3)$ After simplification : $f'(2.3) = 11.27$ b) $f(x) = \frac{x}{x^{2}+1}$ $f'(x) = \frac{(x^{2}+1)(1)-x(2x)}{(x^{2}+1)^{2}}$ $f'(x) = \frac{1-x^{2}}{(x^{2}+1)^{2}}$ $f'(x_{0}) = \frac{1-(x_{0})^{2}}{((x_{0})^{2}+1)^{2}}$ As $x_{0} = -0.5$ $f'(-0.5) = \frac{1-(-0.5)^{2}}{((-0.5)^{2}+1)^{2}}$ After simplification : $f'(-0.5) = 0.48$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.