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UPSC NDA Math Model Paper 2

Comprehension:(Que No. 105 - 106)

For the next two (02) items that follow:

Consider the function

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

Question : 106 of 120

Marks: +1, -0

The function f(x) is a decreasing function in the interval

Solution:

Given:

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

Differentiating, both sides, we get

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

For

f(x)

to be increasing function,

\therefore f'(x)>0

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

\Rightarrow -6(x^{2}+3 x+2)>0

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

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

∴ x ∈ (-∞, -2) ∪ (-1, ∞)

∴ Option 4 is correct.

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