IIT-JEE 2007 · Paper 2 · Mathematics Q56

← IIT-JEE 2007 · Paper 2

MathematicsAssertion and reason+3 / -1Question 56 of 66

Let $f(x)=2+\cos x$ for all real $x$ .

STATEMENT-1: For each real $t$ , there exists a point $c$ in $[t,t+\pi]$ such that $f'(c)=0$ .

because

STATEMENT-2: $f(t)=f(t+2\pi)$ for each real $t$ .

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

Statement-1 is True, Statement-2 is False

Statement-1 is False, Statement-2 is True

Answer and worked solution

Official answer: B

Statement 1. $f'(c)=-\sin c=0$ at $c=k\pi$ . Any closed interval $[t,t+\pi]$ of length π contains a multiple of π. True.

Statement 2. $\cos$ has period 2π, so $f(t)=f(t+2\pi)$ . True, but periodicity with period 2π does not give a critical point in every interval of length π (Rolle on $[t,t+2\pi]$ only guarantees one in an interval of length 2π).

(B)

Topics:Rolle's and mean value theorems Trigonometric equations

← Previous question Next question →

IIT-JEE 2007 · Paper 2, Mathematics question 56