If the slope of the curve y=axb−x at the point (1,1) is 2 then

If the slope of the curve y=axbx at the point (1,1) is 2 then

  1. A

    a=1, b=2

  2. B

    a=1, b=2

  3. C

    a=1, b=2

  4. D

    none of these

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    Solution:

    We have,

    y=axbxdydx=(bx)a+ax(bx)2dydx=ab(bx)2 dydx(1,1)=ab(b1)2ab(b1)2=2

    Since, (1, 1) lies on (i). Therefore,

    1=ab1

    From (ii) and (iii), we have

    bb1=2b=2

    Putting b = 2 in (iii), we get a = 1.

    Hence, a = 1. and b = 2

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