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UPSC NDA II 2025 Mathematics Paper

Question Numbers: 87-88

For the following two (02) items:

Let the function f(x) = | x - 3 | + | x - 4 | be defined on the interval [0, 5].

Question : 88 of 120

Marks: +1, -0

x = 3

x = 4

Which of the statements given above is/are correct?

Solution:

Concept:

A function is differentiable at a point only if its left-hand derivative (LHD) equals its right-hand derivative (RHD) at that point.

Explanation:

x=3

, LHD

=-2

and RHD

=0

. Since they are not equal, the function is not differentiable at

x=3

x=4

, LHD

=0

and RHD

=2

. They are also unequal, so the function is not differentiable at

x=4

Thus, both statements I and II are false.

Answer:

D. Neither I nor II

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