Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.4 Exercises - Page 136: 69



Work Step by Step

Using the quotient rule: $f'(t)=(\frac{u(t)}{v(t)})'=\frac{u'(t)v(t)-v'(t)u(t)}{(v(t))^2}$. $u(t)=3t+2 ;u'(t)=3$. $v(t)=t-1 ;v'(t)=1$. $f'(t)=\dfrac{3(t-1)-1(3t+2)}{(t-1)^2}=-\dfrac{5}{(t-1)^2}$. $f'(0)=-\dfrac{5}{(0-1)^2}=-5.$ A graphing utility was used to verify this result.
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