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BITSAT 2019

Exam: BITSAT
Year: 2019
Subject: Mathematics
Chapter: Differentiation

BITSAT 2019 · Mathematics · Differentiation

Let f ( x ) = x [x], x Z , ( [ · ] denotes greatest integer...

Let

f ( x ) = x \left[x\right], x \notin Z

, (

[ \cdot ]

denotes greatest integer function), then

f^{'}\left(x\right) is equal to

Options

A $2x$
B $\left[x\right]$
C $2 \left[x\right]$
D $1$

Correct answer

B. $\left[x\right]$

Step-by-step solution

We have, $f ( x ) = x \left[x\right]$

$∴ \left[x\right]$ is an integer.

$⇒ f \left(x\right) = px \left[∵ [ x ] = p\right]$

$⇒ f^{'} \left(x\right) = p = \left[x\right]$

$∴ f^{'} \left(x\right) = \left[x\right]</p>$

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