A) \[[1,\,\,12]\]
B) \[[12,\,\,34]\]
C) \[[35,\,\,50]\]
D) \[[-12,\,\,12]\]
Correct Answer: B
Solution :
Given,\[f(x)={{x}^{3}}+3x-2\] On differentiating w.r.t. x, we get, \[f(x)=3{{x}^{2}}+3\] Put \[f(x)=0\] \[\Rightarrow \] \[3{{x}^{2}}+3=0\] \[\Rightarrow \] \[{{x}^{2}}=-1\] \[\therefore \] \[f(x)\]is either increasing or decreasing. At\[x=2,\,\,f(2)={{2}^{3}}+3(2)-2=12\] At\[x=3,\,\,f(3)={{3}^{3}}+3(3)-2=34\] \[\therefore \]\[f(x)\in [12,\,\,34]\]
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