Answer:
We have, \[f(x)={{x}^{3}}-3{{x}^{2}}+3x-100\] On differentiating both sides w.r.t. x, we get \[f'(x)=3{{x}^{2}}-6x+3=3({{x}^{2}}-2x\,+1)\] \[={{(x\,-1)}^{2}}\ge 0,\] for real values of x. \[\therefore \]f(x) is increasing in R . Hence proved.
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