#### Answer

$f(\frac{1}{2})=f(2)=\frac{5}{2}$ and c=1

#### Work Step by Step

$f(\frac{1}{2})= \frac{1}{2}+\frac{2}{1}=\frac{5}{2}$
$f(2)=2+\frac{1}{2}= \frac{5}{2}$
We have
$f(\frac{1}{2})=f(2)=\frac{5}{2}$
f'(x)= $1-\frac{1}{x^{2}}$
Now let c be a point in $(\frac{1}{2},2)$ and let f'(c) be 0.
That is, $1-\frac{1}{c^{2}}=0$
⇒ 1=$\frac{1}{c^{2}}$ or $c^{2}=1$
⇒ c= 1.