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Question

Which of the following is (are) true about the function f (x) = 4x3 18x2 + 27x 7 ?

A
Has a maxima at x = 3/2
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B
x = 3/2 is a point of inflexion
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C
Has a minima at x = 3/2
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D
Neither has a maxima nor minima
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Solution

The correct option is D Neither has a maxima nor minima
f (x)=4x318x2+27x7 f ' (x) = 12x236x+27 f ' (x) =3(4x212x+9)=3 (2x 3)2 f ' (x) = 0 x = 32 (critical point) Since f ' (x) > 0 for all x<32 and for all x>32 Hence x=32 is a point of inflexion i.e., neither a point of maxima nor a point of minima. x = 32 is the only critical point, and f has neither maxima nor minima.

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