$f'(x)= \sqrt x$
$f(x) =\int \sqrt x dx $
$\qquad =\large\frac{x^{1/2+1}}{1/2+1}$$+c$
$f(x) =\large\frac{2}{3} $$x^{3/2} +c$
$f(1)= \large\frac{2}{3} $$ \times 1 +c$
$2= \large\frac{2}{3} $$+c$
$c= 2 - \large\frac{2}{3}$
$\quad= \large\frac{6-2}{3} =\frac{4}{3}$
$f(x) =\large\frac{2}{3} $$x^{2/3} +\large\frac{4}{3} $
$\qquad= \large\frac{2}{3} $$ (x \sqrt x +2)$
Hence 3 is the correct answer.