A) \[\frac{3+\sqrt{3}}{3}\]
B) \[\frac{3+\sqrt{2}}{2}\]
C) \[1+\sqrt{2}\]
D) \[\sqrt{2}\]
Correct Answer: A
Solution :
Given, \[f(x)={{x}^{3}}-3{{x}^{2}}+2x+10\] On differencing w.r.t.x, we get \[f'(x)=3{{x}^{2}}-6x+2\] Put \[f'(x)=0\] \[3{{x}^{2}}-6x+2=0\] \[\Rightarrow \] \[x=\frac{6\pm \sqrt{36-24}}{2\times 3}\] \[\Rightarrow \] \[x=\frac{6\pm 2\sqrt{3}}{2\times 3}\] \[\Rightarrow \] \[x=\frac{3+\sqrt{3}}{2}\]\[\left( \begin{align} & \because \,\,x=\frac{3-\sqrt{3}}{2}\,\text{does}\,\text{not lie in } \\ & \text{the given interval}\, \\ \end{align} \right)\]
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