\(f\left(1\right)=0\)
\(\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-f\left(1\right)}{x-1}=\lim\limits_{x\rightarrow1}\dfrac{\sqrt{x^3-2x^2+x+1}-1}{\left(x-1\right)^2}\)
\(=\lim\limits_{x\rightarrow1}\dfrac{x\left(x-1\right)^2}{\left(x-1\right)^2\left(\sqrt{x^3-2x^2+x+1}+1\right)}\)
\(=\lim\limits_{x\rightarrow1}\dfrac{x}{\sqrt{x^3-2x^2+x+1}+1}=\dfrac{1}{\sqrt{1-2+1+1}+1}=\dfrac{1}{2}\)
Vậy \(f'\left(1\right)=\dfrac{1}{2}\)
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