# Area of a triangle under a curve

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1. Nov 22, 2015

### diredragon

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. Nov 22, 2015

### pasmith

You have the width and height of the triangle in terms of $x_0$. That then gives you the area in terms of $x_0$, which you can maximize.

3. Nov 22, 2015

### Staff: Mentor

Side note -- "axises" is not a word in English. The plural of "axis" is "axes".
One axis, two axes.

4. Nov 22, 2015

### diredragon

So i take (d/dxo)((e^(-xo))*(xo + 1)^2) and whatever i get is the value of the maximum area right?

5. Nov 23, 2015

### diredragon

Solved it. Thanks!

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