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Math Help - Tangent on a curve

  1. #1
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    Post Tangent on a curve

    It's really hard for me to solve this problem. I would be gratefull if anybody could help me.

    A tangent is drawn from point P on the curve y = 4 / x in the first quadrant. This limit together with the coordinate axes a triangle. Show that the area of this triangle is independent of the choice of P.
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  2. #2
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    Quote Originally Posted by hejmh View Post
    It's really hard for me to solve this problem. I would be gratefull if anybody could help me.

    A tangent is drawn from point P on the curve y = 4 / x in the first quadrant. This limit together with the coordinate axes a triangle. Show that the area of this triangle is independent of the choice of P.
    Start by setting P=(x_1,y_1). Then differentiate y=4/x and work out the equation of the tangent.
    Can you work out the general area of the triangle from this?
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