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Question

Which of the following is (are) true about the function f(x)=34x48x3452x2+105 ?

A
x = 0 is point of local maxima
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B
x = 0 is point of local minima
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C
x = –3 is point of local minima
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D
x = –5 is point of local maxima.
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E
x = –5 is point of local minima.
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Solution

The correct option is D x = –5 is point of local maxima.
f'(x)=3x324x245x=3x(x2+8x+15)f'(x)=3x(x+3)(x+5)f'(x)=0x=0, 3, 5f''(x)=9x248x45=3(3x2+16x+15)f''(0)=45<0.Therefore, x = 0 is point of local maximaf''(3)=18>0Therefore, x = 3 is point of local minimaf''(5)=30<0Therefore, x = 5 is point of local maxima.

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