Answer
$y=\frac{1}{2}x+\frac{1}{2}$
Work Step by Step
$y=\sqrt x ,(1,1)$
1. Find the first derivative by using the power rule. Finding the first derivative gives you the slope of the tangent line.
$y'=\frac{1}{2\sqrt x}$
2. Plug in the given x value to find the slope of the tangent line to the curve at the given point.
$y'=\frac{1}{2\sqrt 1}$
$y'=\frac{1}{2}$
3. Now that we have the slope of the tangent line, we can write the equation for that line in point-slope form.
$y-y_{1}=m(x-x_{1})$
$y-1=\frac{1}{2}(x-1)$
4. Rewrite into standard form by distributing the 1/2 and adding one to both sides.
$y-1+1=\frac{1}{2}x-\frac{1}{2}+1$
5. Clean up and simplify.
$y=\frac{1}{2}x+\frac{1}{2}$
