Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.2 The Derivative as a Function - Preliminary Questions - Page 113: 2

Answer

$(f-g)'(1)$ =-2. $ (3f + 2g)'(1) $ = 19.

Work Step by Step

Derivative properties state that $(f-g)'$ = $f' - g'$ and $(f+g)'$ = $f' + g'$. Thus, $(f-g)'(1)$ = $ f'(1) - g'(1) $ = 3 - 5 = -2. $ (3f + 2g)'(1) $ = $ 3f'(1) + 2g'(1)$ = 3 (3) + 2 (5) = 19.
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