A) \[f(x)\] has minimum at \[x=1\]
B) \[f(x)\] has maximum at \[x=6\]
C) \[f(x)\]has maximum at \[x=1\]
D) \[f(x)\] has no maxima or minima
Correct Answer: C
Solution :
\[f(x)=2{{x}^{3}}-21{{x}^{2}}+36x-30\Rightarrow f'(x)=6{{x}^{2}}-42x+36\] \[\therefore f'(x)=0\Rightarrow x=6,\ 1\]and \[{f}''\,(x)=12x-42\] Here \[{f}''\,(1)=-30\] and \[{f}''\,(6)=30\] Hence \[f(x)\]has maxima at \[x=1\]and minima at \[x=6\].
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