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For 0 lt r lt 1, let n(r) dennotes the l...

For `0 lt r lt 1,` let `n_(r)` dennotes the line that is normal to the curve `y = x ^r` at the point `(1,1)` Let `S _(r)` denotes the region in the first quadrant bounded by the curve `y = x ^(r )` ,the x-axis and the line `n _(r )'` Then the value of r the minimizes the area of ` S_(r )` is :

A

`(1)/(sqrt2)`

B

`sqrt2-1`

C

`(sqrt2-1)/(2)`

D

`sqrt2-1/2`

Text Solution

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The correct Answer is:
B
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