Notes on a WebWork problem

Suppose we want to find the maximum area of a triangle formed in the first quadrant by the x-axis, the y-axis and a tangent line to the graph of maxTriangle_1.png. I guess the situation looks like so:

maxTriangle_2.gif

maxTriangle_3.png

maxTriangle_4.gif

Here are some relevant computations:

maxTriangle_5.gif

maxTriangle_6.png

maxTriangle_7.png

maxTriangle_8.png

maxTriangle_9.png

maxTriangle_10.png

maxTriangle_11.png

Created with the Wolfram Language