Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.4 - Average Rate of Change of a Function - 2.4 Exercises - Page 188: 23

Answer

a) $\dfrac{-2h}{a(a+h)}$ b) $\dfrac{-2}{a(a+h)}$

Work Step by Step

a) Apply the rule such as: $f(b)-f(a)$ where $a \leq by$ Thus, the net change is given as: $f(b)-f(a)=f(a+h)-f(h)$ This gives: $\dfrac{2}{a+h}-\dfrac{2}{a}=\dfrac{2a-2a-2h}{a(a+h)}=\dfrac{-2h}{a(a+h)}$ b) Apply the rule such as: $f(b)-f(a)$ where $a \leq by$ Thus, the net change is given as: $\dfrac{f(b)-f(a)}{b-a}=\dfrac{f(a+h)-f(a)}{(a+h)-a}$ This gives: $\dfrac{2/a+h-2/a}{a+h-a}=\dfrac{\dfrac{-2h}{a(a+h)}}{h}=\dfrac{-2}{a(a+h)}$
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