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Let f(x)=(sinpix)/(x^(2)), x gt 0 The ...

Let `f(x)=(sinpix)/(x^(2)), x gt 0`
The `x_(1) lt x_(2) lt x_(3) . . . lt x_(n)lt .. . ` be all points of local maximum of f(x) and `y^(1) lt y_(2) lt y_(3) . . . lt y_(n) lt . . .` be all the points of lcal minimum of f(x) then correct options is/are

A

`|x_(n)-y_(n)|gt 1 ` for every n

B

`x_(1) lt y_(1)`

C

`x_(n) in (2n, 2n+(1)/(2))` for every n

D

`x_(n+1)-x_(n)gt2` for every n

Text Solution

Verified by Experts

The correct Answer is:
A, C, D

`f'(x)=(2xcospix((pix)/(2)-tanpix))/(x^(4))`
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