\(\lim\limits_{x\rightarrow1^-}=f\left(1\right)=\lim\limits_{x\rightarrow1^-}\sqrt{4-x^2}=\sqrt{3}\)
\(\lim\limits_{x\rightarrow1^+}f\left(x\right)=\lim\limits_{x\rightarrow1^+}\left(x^2+bx+c\right)=b+c+1\)
Để hàm số liên tục tại x=1 \(\Rightarrow b+c+1=\sqrt{3}\)
\(f'\left(1^-\right)=\lim\limits_{x\rightarrow1^-}\frac{-x}{\sqrt{4-x^2}}=-\frac{1}{\sqrt{3}}\)
\(f'\left(1^+\right)=\lim\limits_{x\rightarrow1^+}\left(2x+b\right)=b+2\)
Để hàm số có đạo hàm tại \(x=1\)
\(\Leftrightarrow\left\{{}\begin{matrix}b+c+1=\sqrt{3}\\b+2=-\frac{1}{\sqrt{3}}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}b=-2-\frac{1}{\sqrt{3}}\\c=1+\frac{4}{\sqrt{3}}\end{matrix}\right.\)
