Question

Determine the average rate of change of the function between the given values of the variable. f(t)=2/t; t=a, t=a+h

Answer 1

Average rate of change = \(\large \frac{f(a+h)-f(a)}{(a+h)-(a)}=\frac{\frac{2}{a+h}-\frac{2}{a}}{(a+h)-(a)} \)

simplify....

Answer 2

i get to [2a-2(a+h)]/h and simplify to 1, but the book says -2/(a(a+h))

Answer 3

\[\huge \frac{f(a+h)-f(a)}{(a+h)-(a)}=\frac{\frac{2}{a+h}-\frac{2}{a}}{(a+h)-(a)} \]
\[\huge =\frac{\frac{2}{a+h}\cdot\frac{a}{a}-\frac{2}{a}\cdot \frac{a+h}{a+h}}{(a+h)-(a)} \]
\[\huge =\frac{\frac{2a-2(a+h)}{a(a+h)}}{h} \]
\[\huge =\frac{\frac{2a-2a-2h}{a(a+h)}}{h} \]
\[\huge =\frac{\frac{-2h}{a(a+h)}}{h} \]
\[\huge =\frac{\frac{-2 \cancel h}{a(a+h)}}{\cancel h} \]
\[\huge =\frac{-2}{a(a+h)} \]