Answer
$y=-\dfrac {1}{4}x+1$
Work Step by Step
Lets assume that equation of line that if tangent to this function is:
$y=ax+b$ At that point $(2,1/2)$
İf it is tangent to function then $f'\left( x\right) =a$
$f’\left( x\right) =\left( \dfrac {1}{x}\right) ‘=( x^{-1} )’=-1\times x^{-1-1}=-\dfrac {1}{x^{2}}$
$f'\left( 2\right) =-\dfrac {1}{2^{2}}=a=-\dfrac {1}{4}$
$y=ax+b\Rightarrow \dfrac {1}{2}=-\dfrac {1}{4}\times 2+b\Rightarrow b=1$
So the equation will be:
$y=-\dfrac {1}{4}x+1$
