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UPSC NDA 2 2016 Mathematics Solved Paper

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Consider the following function for the next two (02) items that follow:

f(x)=\begin{cases} 3x^{2}+12x-1, & -1 \le x \le 2 \\ 37-x, & 2 < x \le 3 \end{cases}.

[NDA II 2016]

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Question : 76 of 120

Marks: +1, -0

Which of the following statement is/are correct?

f(x)

is increasing in the interval

[-1,2]

f(x)

is decreasing in the interval

(2,3]

Select the correct answer using the code given below:

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Solution:

For

-1\leq x\leq 2

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

f'(x)=6x+12

If we take any point in the interval

[-1,2]

then

f'(1)=6\times 1+12=18>0

\Rightarrow f(x)

is increasing in the interval

[-1,2]

.

For

2 < x \leq 3

f(x)=37-x

f'(x)=-1<0

\Rightarrow f(x)

is decreasing in the interval

(2,3]

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