jee-advanced 2007 Q47

jee-advanced · India · paper1 Proof True/False Justification
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 $t$.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
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 $t$.\\
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1\\
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1\\
(C) Statement-1 is True, Statement-2 is False\\
(D) Statement-1 is False, Statement-2 is True