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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.

No one has answered this question yet.

Yes it is the right equation. Good job!

is the max. area 3.6945?
thanks.

Yes, that's correct too.

In exams and in general, if the number is a "round" number like e⊃2/2, I would give the answer as e²/2=3.6945(approx.)
because the latter is an approximation. This will give the exact value as the answer.

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