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Area of a triangle under a curve

  1. Nov 22, 2015 #1
    1. The problem statement, all variables and given/known data
    The tangent line of a curve y=e^(-x) intercepts the axises at points A and B. What is the maximum area of a triangle AOB considering O as the origin.

    2. Relevant equations
    Ar= xy/2

    3. The attempt at a solution
    Derivative of this function is y'=-e^(-x)
    I took the formula of the tangent line
    y - yo = -e^(-x)(x-xo) and solved for x=0 and y=0 getting two equations
    y = (xo + 1)yo and x = 1+ xo yet i dont know where to follow from this
    Last edited by a moderator: Nov 22, 2015
  2. jcsd
  3. Nov 22, 2015 #2


    User Avatar
    Homework Helper

    You have the width and height of the triangle in terms of [itex]x_0[/itex]. That then gives you the area in terms of [itex]x_0[/itex], which you can maximize.
  4. Nov 22, 2015 #3


    Staff: Mentor

    Side note -- "axises" is not a word in English. The plural of "axis" is "axes".
    One axis, two axes.
  5. Nov 22, 2015 #4
    So i take (d/dxo)((e^(-xo))*(xo + 1)^2) and whatever i get is the value of the maximum area right?
  6. Nov 23, 2015 #5
    Solved it. Thanks!
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