A) Maximum at \[x=3\]and minimum at \[x=1\]
B) Minimum at \[x=1\]
C) Neither maximum nor minimum at \[x=0\]
D) Maximum at \[x=0\]
Correct Answer: C
Solution :
Let\[f(x)={{x}^{5}}-5{{x}^{4}}+5{{x}^{3}}-1\] Þ \[f'(x)=5{{x}^{4}}-20{{x}^{3}}+15{{x}^{2}}=0\] \[\therefore (x-3)(x-1)=0\] or \[x=3,1\] Now \[{f}''(x)=20{{x}^{3}}-60{{x}^{2}}+30x\] Put \[x=3\] and 1, we get \[{f}'''(3)=+ve\]and \[{f}''(1)=-ve\] and \[{f}''(0)=0\]. Hence \[f(x)\] neither maximum nor minimum at \[x=0\].
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