Calculus 10th Edition

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

Chapter 2 - Differentiation - Review Exercises: 25

Answer

(a) F'(4) = 50 vibrations/sec/lb (b) F'(9) = $\frac{100}{3}$ or 33 $\frac{1}{3}$ vibrations/sec/lb

Work Step by Step

F = 200$\sqrt T$ F(t) = 200$T^{\frac{1}{2}}$ F'(t) = 200($\frac{1}{2})T^{-\frac{1}{2}}$ F'(t) = $\frac{100}{\sqrt T}$ (a) When T = 4: F'(4) = $\frac{100}{\sqrt 4}$ F'(4) = $\frac{100}{2}$ F'(4) = 50 vibrations/sec/lb (b) When T = 9: F'(4) = $\frac{100}{\sqrt 9}$ F'(4) = $\frac{100}{3}$ vibrations/sec/lb
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