find the particular solution of the equation f'(x)=2x^(-1/2) that satisfies the condition f(1)=6

find the particular solution of the equation f'(x)=2x^(-1/2) that satisfies the condition f(1)=6

$$\\f'(x)=2x^{-1/2 }\\\\ f(x)=\int\;2x^{-1/2 }dx\;\\\\ f(x)=\;\dfrac{2x^{+1/2 }}{1/2}+c\\\\ f(x)=4\sqrt{x}+c\\\\ but\\ f(1)=6\\\\ so\\ 6=4\sqrt{1}+c\\\\ 6=4+c\\\\ c=2\\\\ so\\ f(x)=4\sqrt{x}+2\\\\$$