Answer
$y=2x+\frac{1}{4}$
Work Step by Step
Equation of the tangent line to the curve $y=f(x)$ at the point $a$ is of the form
$y=f(a)+f'(a)(x-a)$
Given that $f(x)=x+\sqrt x$ and
Slope=$f'(a)=1+\frac{1}{2\sqrt a}=2$
$\implies \sqrt a=\frac{1}{2}$ or $a=\frac{1}{4}$
Then, $f(a)=f(\frac{1}{4})=\frac{1}{4}+\sqrt {\frac{1}{4}}=\frac{3}{4}$
Therefore, the equation of the tangent line is
$y=\frac{3}{4}+2(x-\frac{1}{4})$
Or $y=2x+\frac{1}{4}$
