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calculus

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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.

  • calculus -

    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.

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