The point on the curve y=12x−x2 where the tangent is parallel to x-axis, is

The point on the curve y=12xx2 where the tangent is parallel to x-axis, is

  1. A

    (0, 0)

  2. B

    (2,16)

  3. C

    (3, 9)

  4. D

    (6, 36)

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    Solution:

    Let x1, y1 be the required point on y=12xx2

    Then,

    dydxx1,y1=0122x1=0x1=6y=12xx2dydx=122x

    Since x1, y1 lies on y=12xx2

     y1=12x1x12y1=7236=36

    Hence, ( 6, 36) is the required point

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