JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

Let

f(x)=[x] \sin (\pi x)

where

[x]

denotes the integer part of

x

. Then at

x=k, k

being an integer, the left derivative of

f(x)

View answer and explanation

Correct option: A

(-1)^k(k-1) \pi

Option A (

(-1)^k(k-1) \pi

) is correct because it is the result of calculating the left derivative of the function at x=k using the limit definition.

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f(x)=|x|^{|\tan x|}

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x

y

x>0

x y=1

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