jee-advanced 2013 Q53

jee-advanced · India · paper1 Applied differentiation Existence and number of solutions via calculus

Let $f ( x ) = x \sin \pi x , x > 0$. Then for all natural numbers $n , f ^ { \prime } ( x )$ vanishes at
(A) a unique point in the interval $\left( n , n + \frac { 1 } { 2 } \right)$
(B) a unique point in the interval $\left( n + \frac { 1 } { 2 } , n + 1 \right)$
(C) a unique point in the interval $( n , n + 1 )$
(D) two points in the interval $( n , n + 1 )$

Let $f ( x ) = x \sin \pi x , x > 0$. Then for all natural numbers $n , f ^ { \prime } ( x )$ vanishes at\\
(A) a unique point in the interval $\left( n , n + \frac { 1 } { 2 } \right)$\\
(B) a unique point in the interval $\left( n + \frac { 1 } { 2 } , n + 1 \right)$\\
(C) a unique point in the interval $( n , n + 1 )$\\
(D) two points in the interval $( n , n + 1 )$

Paper Questions

Q41 Q42 Q43 Q44 Q45 Q46 Q47 Q48 Q49 Q50 Q51 Q52 Q53 Q54 Q55 Q56 Q57 Q58 Q59 Q60