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UPSC NDA I 2023 Mathematics Solved Paper

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Question Numbers: 86-88

Consider the following for the next three (03) items that follow :

Let f(x) = | ln x | , x ≠ 1

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Question : 87 of 120

Marks: +1, -0

What is the derivative of f(x) at

x = 2

?

$-\frac{1}{2}$
$-1$
$\frac{1}{2}$
2

Solution:

Concept:

The derivative of

f(x) = |\ln x|

at

x=2

is found by considering the sign of

\ln x

near

x=2

.

Explanation:

Since

x=2 > 1

,

\ln 2 > 0

.

Therefore,

f(x) = \ln x

for

x>1

.

The derivative of

\ln x

is

\frac{1}{x}

.

At

x=2

,

f'(2) = \frac{1}{2}

.

Answer:

\frac{1}{2}

(Option C)

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