Calculus 10th Edition

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

Chapter 3 - Applications of Differentiation - 3.3 Exercises: 92

Answer

False.

Work Step by Step

Let $h(x)=f(x)\times g(x)$ and $f'(x)gt;0; g'(x)gt;0$ over some interval $(a, b).$ Then $h'(x)=f'(x)g(x)+g'(x)f(x)$ which is not necessarily positive over the interval $(a, b)$ since we do not know the values of $f(x)$ and $g(x).$
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