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What is the average rate of change of
$g(x)=\frac{2}{x+3}$
g(x)=(2)/(x+3)
over the interval
$1\le x\le 3$
1 <= x <= 3
?
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Best Answer
The average rate of change of
$g(x)=\frac{2}{x+3}$
g(x)=(2)/(x+3)
over the interval
$1\le x\le 3$
1 <= x <= 3
is given by the formula:
$$\frac{g(3)-g(1)}{3-1}$$
(g(3)-g(1))/(3-1)
We need to compute
$g(3)$
g(3)
and
$g(1)$
g(1)
:
$$g(3)=\frac{2}{3+3}=\frac{1}{3}$$
g(3)=(2)/(3+3)=(1)/(3)
$$g(1)=\frac{2}{1+3}=\frac{1}{2}$$
g(1)=(2)/(1+3)=(1)/(2)
Substituting these values, we get:
$$\frac{g(3)-g(1)}{3-1}=\frac{\frac{1}{3}-\frac{1}{2}}{2}=\frac{-1}{6}$$
(g(3)-g(1))/(3-1)=((1)/(3)-(1)/(2))/(2)=(-1)/(6)
Therefore, the average rate of change of
$g(x)=\frac{2}{x+3}$
g(x)=(2)/(x+3)
over the interval
$1\le x\le 3$
1 <= x <= 3
is
$\overline{){\displaystyle \frac{-1}{6}}}$
(-1)/(6)
.
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