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Question

If f(x)=(x3)5(x+1)4, then which of the following is/are NOT CORRECT ?

A
x=79 is a point of local maxima
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B
x=3 is a point of local minimum
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C
f has no point of local maxima
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D
x=1 is a point of local maxima
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Solution

The correct option is C f has no point of local maxima
f(x)=(x3)5(x+1)4
f(x)=4(x3)5(x+1)3+5(x+1)4(x3)4
=(x3)4(x+1)3(4x12+5x+5)
=(x3)4(x+1)3(9x7)
From f(x)=0
x=1,3,79

From the above sign change of f(x)
x=1 is the point of local maxima,
x=79 is the point of local minima,
At x=3 neither minima nor maxima.

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