JEE Advanced | 2013Application of DerivativeHard
Question
Let f(x) = x sin π x, x > 0. Then for all natural numbers n, f′(x) vanishes at -
Options
A.a unique point in the interval 
B.a unique point in the interval 
C.a unique point in the interval (n, n + 1)
D.two points in the interval (n,n + 1)
Solution
Æ’′(x) = sinπx + π x cos π x = 0
tan π x = - p x
y = tanx π & y = - π x
intersection point lies in
..........
as well (n, (n + 1)) because root lies in
tan π x = - p x
y = tanx π & y = - π x
intersection point lies in
..........as well (n, (n + 1)) because root lies in
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