find the particular solution of the equation f'(x)=2x^(-1/2) that satisfies the condition f(1)=6
+118723 find the particular solution of the equation f'(x)=2x^(-1/2) that satisfies the condition f(1)=6
$$\\f'(x)=2x^{-1/2 }\\\\
f(x)=\int\;2x^{-1/2 }dx\;\\\\
f(x)=\;\dfrac{2x^{+1/2 }}{1/2}+c\\\\
f(x)=4\sqrt{x}+c\\\\
but\\
f(1)=6\\\\
so\\
6=4\sqrt{1}+c\\\\
6=4+c\\\\
c=2\\\\
so\\
f(x)=4\sqrt{x}+2\\\\$$
+118723 find the particular solution of the equation f'(x)=2x^(-1/2) that satisfies the condition f(1)=6
$$\\f'(x)=2x^{-1/2 }\\\\
f(x)=\int\;2x^{-1/2 }dx\;\\\\
f(x)=\;\dfrac{2x^{+1/2 }}{1/2}+c\\\\
f(x)=4\sqrt{x}+c\\\\
but\\
f(1)=6\\\\
so\\
6=4\sqrt{1}+c\\\\
6=4+c\\\\
c=2\\\\
so\\
f(x)=4\sqrt{x}+2\\\\$$
