Area of a triangle under a curve

[diredragon]

Homework Statement

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.

Homework Equations

Ar= xy/2

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 don't know where to follow from this

 

[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.

 

[Mark44]

The tangent line of a curve y=e^(-x) intercepts the axises at points A and B.

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

 

[diredragon]

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.

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

 

[diredragon]

Solved it. Thanks!