Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 3 - Applications of Differentiation - 3.1 Maximum and Minimum Values - 3.1 Execises: 36

Answer

The critical numbers are $p=1\pm \sqrt 5$

Work Step by Step

Find the critical values of this function $h(p)=\frac{p-1}{p^2+4}$ Differentiate and set the derivative $=0$ $h'(p) = \frac{p^2+4-2p(p-1)}{(p^2+4)^2}$ Critical numbers exist where the derivative $= 0$. The derivative $= 0$ when the numerator $= 0$ $0=p^2+4-2p^2+2p$ $0=-p^2+2p+4$ Solve for $p$ with the quadratic formula $p=1\pm \sqrt 5$
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