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Trigonometric Functions and Equations question

2013 · Shift 1 · Q21

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JEE Advanced
Mathematics
Trigonometric Functions and Equations
2013 · Shift 1 · Q21

Trigonometric Functions and Equations question

2013 · Shift 1 · Q21

JEE AdvancedMathematicsTrigonometric Functions and EquationsMultiple correct+4 / −1

Let

f\left( x \right) = x\sin \,\pi x,\,x \gt 0.

Then for all natural numbers

n,\,f'\left( x \right)

vanishes at

A
A unique point in the interval $\left( {n,\,n + {1 \over 2}} \right)$
B
A unique point in the interval $\left( {n + {1 \over 2},n + 1} \right)$
C
A unique point in the interval $\left( {n,\,n + 1} \right)$
D
Two points in the interval $\left( {n,\,n + 1} \right)$

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