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Question

f(x)=x33x2+6x+7 has

A
a minimum only
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B
neither maximum nor minimum
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C
a maximum only
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D
a maximum and a minimum
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Solution

The correct option is B neither maximum nor minimum
f(x)=x33x2+6x+7
f(x)=3x26x+6
D=624(3)(6)=36<0
So,f(x) will be always positive f(x) will be an increasing function.
Hence, f(x) has neither maximum nor minimum.

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