Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.5 Higher Derivatives - Exercises - Page 135: 24



Work Step by Step

Since $ f(t)=\frac{t}{t+1}$, then we get $$ f'(t)=\frac{(t+1)-t}{(t+1)^2}=\frac{1}{(t+1)^2}, \quad f''(t)=-\frac{2}{(t+1)^3}.$$ Hence, $ f''(1)=-\frac{2}{(1+1)^3}=-\frac{1}{4}$.
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