1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Area of a triangle under a curve

  1. Nov 22, 2015 #1


    User Avatar
    Gold Member

    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


    User Avatar
    Gold Member

    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


    User Avatar
    Gold Member

    Solved it. Thanks!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted