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UPSC NDA II 2015 Mathematics Solved Paper

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For the next two items that follows:

Consider the function

f(x)=-2x^3-9x^2-12x+1

[NDA II 2015]

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Question : 95 of 120

Marks: +1, -0

The function f(x) is an increasing function in the interval ?

$(-2,-1)$
$(-\infty,-2)$
$(-1,2)$
$(-1,\infty)$

Solution:

f(x)=-2x^{3}-9x^{2}-12x+1

f'(x)=-6x^{2}-18x-12

for increasing function

f'(x) > 0

\Rightarrow -(6x^{2}+18x+12)>0

\Rightarrow (x^{2}+3x+2)<0

\Rightarrow (x+2)(x+1)<0

x=(-2,-1)

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