Consider the function f(x)=|x-2|+|x-5|, x ∈ R . Statement 1 : f^ (4)=0 Statement 2 : f is continuous in [2,5] , differentiable in (2,5) and f(2)=f(5) .

JEE Main 2012Offline

Exam: JEE Main
Year: 2012
Mode: Offline
Subject: Mathematics
Chapter: Continuity and Differentiability

JEE Main 2012 · Offline · Mathematics · Continuity and Differentiability

Consider the function f(x)=|x-2|+|x-5|, x ∈ R . Statement 1 : f^...

Consider the function

f(x)=|x-2|+|x-5|, x \in R

. Statement

1

f^{\prime}(4)=0

Statement

2

f

is continuous in

[2,5]

, differentiable in

(2,5)

and

f(2)=f(5)

Options

AStatement $1$ is false, statement $2$ is true
BStatement $1$ is true, statement $2$ is true; statement $2$ is a correct explanation for statement $1$
CStatement $1$ is true, statement $2$ is true; statement $2$ is not a correct explanation for statement $1$
DStatement $1$ is true, statement $2$ is false

Correct answer

B. Statement $1$ is true, statement $2$ is true; statement $2$ is a correct explanation for statement $1$

Step-by-step solution

f(x) =7-2 x ; x < 2

=3

;

\quad2 \leq x \leq 5

=2 x-7 ; x>5

f(x)

is constant function in

[2,5]

f

is continuous in

[2,5]

and differentiable in

(2,5)

and

f(2)=f(5)

by Rolle's theorem

f^{\prime}(4)=0

\therefore

Statement

2

and statement

1

both are true and statement

2

is correct explanation for statement

1

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