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Math Help - Proof With Area Problem

  1. #1
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    Proof With Area Problem

    enjoy:


    consider the function y = 1/x
    let A be a point on the function
    the tangent through A intersects the coordinate axes at C(c,0) and D(0,d)
    prove that the area of this triangle is the same no matter where A is located and find that area
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  2. #2
    Moo
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    Hello,

    Did you draw a sketch ?

    The area of the triangle OCD is defined by \frac{OD \cdot OC}{2}. Do you agree ?
    Distance OD is d and distance OC is c, so \mathbb{A}=\frac{cd}{2}

    Now, you may know the equation of the tangent to a function. Let m be the absciss of A.
    The equation will be :

    y=f'(m)(x-m)+f(m)

    Knowing that f'(x)=\frac{-1}{x^2}, determine the equation.



    You know that C and D are on this tangent. Hence, replace their coordinates in it and isolate c and d.

    So you will have c=\dots and d=\dots with respect to m.

    Substitute in the expression of \mathbb{A} and conclude




    It's long because I've given all the elements, so try to do and when you can't move on, post
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  3. #3
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    its not that hard is it

    why oh why didnt i write this on my test?

    i managed to do it in 5 minutes on the subway ride home

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  4. #4
    Moo
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    Quote Originally Posted by finch41 View Post
    its not that hard is it

    why oh why didnt i write this on my test?

    i managed to do it in 5 minutes on the subway ride home

    What do you mean ? lol
    It's not really hard, no... You just have to know the definitions..

    I hope this won't penalize you too much...
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