Question

A right triangle has one leg on the x-axis. The vertex at the right end of that leg is at the point (3,0). The other vertex touches the graph os y=e^x. the entire triangle is to lie in the first quadrant. Find the maximum area of this triangle.Justify your answer.

My work:
A= (3-x)y/2
y=e^x
A=(3-x)(e^x)/2 <-- is this the right equation?

Thanks.