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UPSC NDA II 2014 Mathematics Paper

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For the next three (03) items that follow:

Consider the function

f(x)=\begin{cases} x^2-5, & x\le 3 \\ \sqrt{x+13}, & x>3 \end{cases}

[NDA II 2014]

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Question : 63 of 120

Marks: +1, -0

What is the differential coefficient of f(x) at

x=12

5/2
5
1/5
1/10

Solution:

f'(x)=\frac{1}{2\sqrt{x}+13}, x>3

\Rightarrow f'(12)=\frac{1}{2\sqrt{12+13}}=\frac{1}{2\times 5}=\frac{1}{10}

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