Let f(x)=2+ x for all real x . Statement I For each real t , there exists a point c in [t, t+π] such that f^ (c)=0 . Statement II f(t)=f(t+2 π) for each real t .

Correct answer: B. Statement I is True, Statement II is true; Statement II is not a correct explanation for Statement I f(x)=2+ x x ∈ R Statement I There exists a point c ∈[t, t+π] , where f^ (c)=0 Hence, Statement 1 is true. Statement II f(t)=f(t+2 π) is true. But Statement II is not a correct explanation for Statement I.

JEE Advanced 2007Paper 2

Exam: JEE Advanced
Year: 2007
Paper: Paper 2
Subject: Mathematics
Chapter: Application of Derivatives

JEE Advanced 2007 · Paper 2 · Mathematics · Application of Derivatives

Let f(x)=2+ x for all real x . Statement I For each real t , there...

Let

f(x)=2+\cos x

for all real

x

. Statement I For each real

t

, there exists a point

c

[t, t+\pi]

such that

f^{\prime}(c)=0

. Statement II

f(t)=f(t+2 \pi)

for each real

t

Options

AStatement I is true, Statement II is true; Statement II is a correct explanation for Statement I
BStatement I is True, Statement II is true; Statement II is not a correct explanation for Statement I
CStatement I is true, Statement II is false
DStatement I is false, Statement II is true

Correct answer

B. Statement I is True, Statement II is true; Statement II is not a correct explanation for Statement I

Step-by-step solution

f(x)=2+\cos x \forall x \in R

Statement I There exists a point

c \in[t, t+\pi]

, where

f^{\prime}(c)=0

Hence, Statement 1 is true. Statement II

f(t)=f(t+2 \pi)

is true. But Statement II is not a correct explanation for Statement I.

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