Bonjour Noob95
[tex]\boxed{f(x)=a+b\sqrt{x}}\\\\f'(x)=a'+(b\sqrt{x})'=0+b(\sqrt{x})'=b\times\dfrac{1}{2\sqrt{x}}=\dfrac{b}{2\sqrt{x}}\\\\\Longrightarrow \boxed{f'(x)=\dfrac{b}{2\sqrt{x}}}[/tex]
[tex]\left\{\begin{matrix}f(1)=3\\f'(1)=4 \end{matrix}\right.\ \ \ \ \left\{\begin{matrix}a+b\sqrt{1}=3\\\dfrac{b}{2\sqrt{1}}=4 \end{matrix}\right.\ \ \ \ \left\{\begin{matrix}a+b=3\\\dfrac{b}{2}=4 \end{matrix}\right.\ \ \ \ \left\{\begin{matrix}a+b=3\\b=2\times4 \end{matrix}\right.\\\\\\\ \ \ \ \left\{\begin{matrix}a+b=3\\b=8\end{matrix}\right.\ \ \ \ \left\{\begin{matrix}a+8=3\\b=8\end{matrix}\right.\ \ \ \ \left\{\begin{matrix}a=3-8\\b=8\end{matrix}\right.\ \ \ \ [/tex]
[tex]\boxed{\left\{\begin{matrix}a=-5\\b=8\end{matrix}\right}[/tex]
