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Application of Derivatives question

2019 · Shift 2 · Q21

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PYQ Library
JEE Advanced
Mathematics
Application of Derivatives
2019 · Shift 2 · Q21

Application of Derivatives question

2019 · Shift 2 · Q21

JEE AdvancedMathematicsApplication of DerivativesMultiple correct+4 / −1

Let,

f(x) = {{\sin \pi x} \over {{x^2}}}

, x > 0 Let x1 < x2 < x3 < ... < xn < ... be all the points of local maximum of f and y1 < y2 < y3 < ... < yn < ... be all the points of local minimum of f. Then which of the following options is/are correct?

A
$|{x_n} - {y_n}|\, \gt 1$ for every n
B
${x_{n + 1}} - {x_n}\, \gt 2$ for every n
C
x1 < y1
D
${x_n} \in \left( {2n,\,2n + {1 \over 2}} \right)$ for every n

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