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Geometric derivative problem

  1. Dec 31, 2011 #1
    1. The problem statement, all variables and given/known data

    we had a a function on a graph of f(x)=1/x and then we are suposed to find the area of a triangle where the tangent line is the hypontenuse, and the x and y axis are the base and hight.....i found f'(x)= -1/x^2
    from here i used the formula y-yo=x0(x-x0) and got that the x intercept is 2xo and then got the y intercept to be 2yo which means those are the lengths of the base and the hight, from there you use the formula of a triangle and that is (2)(2)(xo)(yo) all over 2 and then i canceled out the 2's and got 2(xo)(yo) as the area of the triangle...and this all is correct...but how the heck does the also = 2??? apperantly 2(Xo)(Yo)=2....could someone please explain this, possibly just some basic algebra rule and i'm having a brain fart???



    by the way, this is off of MIT's OCW.....
     
  2. jcsd
  3. Dec 31, 2011 #2

    SammyS

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    What is y0 in terms of x0 ?

    After all, isn't y0 = f(x0) ?
     
  4. Jan 1, 2012 #3
    yes....but I dont think that makes a difference....you still need some form of units dont you? because if the answer is 2...then its 2 what? 2 inches? 2 meters? I understood it all the way up untill he said therefor it =2
     
  5. Jan 1, 2012 #4

    SammyS

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    The units will cancel.


    The units of y are the reciprocal of the units of x.


    The units of area for this graph are units of x times units of y.
     
  6. Jan 1, 2012 #5
    So I wouldnt be wrong if I left the units then would I? Or is it best to cancle and simplify like that?
     
    Last edited: Jan 2, 2012
  7. Jan 1, 2012 #6

    SammyS

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    The sentence doesn't make sense. Is there a typo ?
     
  8. Jan 2, 2012 #7
    sorry, yes there was some typos....fixed
     
  9. Jan 2, 2012 #8

    SammyS

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    Whatever the units for x, the area of the triangle will not have units. It's a pure number.
     
  10. Jan 2, 2012 #9
    Alright...now that I am thinking about it I think I understand....its because the x's arnt labeled with a unit/number.
     
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