Answer
$y=\dfrac {1}{2}x+\dfrac {1}{2}$
Work Step by Step
Lets assume that Equation for tangent line is :
$y=ax+b$
İf this line is tangent to any $f(x)$ at $(x,y)$ point then
$f’(x)=a$
$f\left( x\right) =\sqrt {x}=\left( x\right) ^{\dfrac {1}{2}}\Rightarrow f'\left( x\right) =\dfrac {1}{2}\times x^{\dfrac {1}{2}-1}=\dfrac {1}{2}x^{-\dfrac {1}{2}}$
$a=f'\left( 1\right) =\dfrac {1}{2}\times 1^{-\dfrac {1}{2}}=\dfrac {1}{2}$
$y=ax+b\Rightarrow 1=\dfrac {1}{2}\times 1+b\Rightarrow b=\dfrac {1}{2}$
So the equation of line is :
$y=\dfrac {1}{2}x+\dfrac {1}{2}$
