The hypotenuse of a right triangle has one end at the origin and one end on the curve y = (x^4)(e^-7x), with x > 0. One of the other two sides is on the x-axis, the other side is parallel to the y-axis. Find the maximum area of such a triangle.

Answer 1

area=1/2 y x

but y=above, so
area=1/2 x^5(e^-7x)

darea/dx=5/2 x^4(e^-7x)-7/2 x^5(e^-7x)=0

divide by x^4 e^-7x
0=5/2 -7/2x
x=5/7
y=you do it, then solve for Area.

check my work.