Calculus

The hypotenuse of a right triangle has one end at the origin and one end on the curve y=x^(7)e^(-7x) , with x greater than or equal to 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. Round your answer to 4 decimal places.
Maximum Area =

At what x-value does it occur?

Any help on these two questions would be greatly appreciated.

  1. 👍 0
  2. 👎 0
  3. 👁 1,511
  1. Area of triangle = 1/2(base)(height)
    = 1/2(x)(x^7)(e^(-7x)
    = 1/2(x^8)(e^(-7x)

    Area' = 1/2[x^8(-7e^(-7x)) + 8x^7(e^(-7x))]
    = 0 for a max/min of Area
    (1/2)e^(-7x)x^7[-7x + 8] = 0
    -7x + 8 = 0
    x = 8/7 or x = 1.142857

    so max area = .000488145

    test: take a slighter larger and a slightly smaller value of x

    if x = 1.14
    area = .000488133

    if x = 1.15
    area = .00048807

    so the largest area correct to 4 decimals is .0005 and it occurs when x = 8/7

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. physics

    the problem reads this "A person with mass m1 = 62 kg stands at the left end of a uniform beam with mass m2 = 93 kg and a length L = 3.5 m. Another person with mass m3 = 65 kg stands on the far right end of the beam and holds a

  2. Algebra

    Which statement about a right triangle is NOT true? A.) The hypotenuse is the longest side of the triangle. B.) The square of the hypotenuse is equal to the sum of the squares of the other two lengths. C.) The sum of the length of

  3. physics

    a 500 N person stands on a uniform board of weight 100 N and length 8 m. the board is supported at each end. if the support force at the right end is three times that at the left end, how far from the right end is the person?

  4. math/calc

    The hypotenuse of a right triangle has one end at the origin and one end on the curve y+x^2e^(-3x), with x > or = 0. One of the other two sides is on the x-asis, the other side is parallel to the y-axis. Find the maximum area of

  1. Physics

    You snap your fingers at the open end of a 1 meter long tube that is closed at the other end. With a microphone at the open end, you determine that it takes 5.8msec between the time you snap your fingers and the echo from the

  2. Math

    Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. The hypotenuse of the largest triangle is 8 centimeters. What is the number of centimeters in the length of the

  3. PLEASE HELP!!!!! (Right Triangle Question)

    Point N is on hypotenuse BC of triangle ABC such than angle CAN is 45 degrees. If AC=8 and AB=6, find AN. I did Pythagorean Theorem for triangle ABC, and hypotenuse BC will be 10. I don't know how to continue from there. Oh, I'm

  4. calculus

    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

  1. Physics

    A person with mass m1 = 57 kg stands at the left end of a uniform beam with mass m2 = 92 kg and a length L = 2.7 m. Another person with mass m3 = 67 kg stands on the far right end of the beam and holds a medicine ball with mass m4

  2. algebra

    Please show solution to this problem. In triangle A, the longer leg is 6 more than the shorter leg and the hypotenuse is 6 more than the longer leg. Find the lengths of each side of this right triangle. Show all calculations.

  3. math

    The angles of a triangle are in the ratio 1:2:3. If its hypotenuse is 12cm, find the volume of the double cone formed by revolution of triangle about its hypotenuse. Pls help me!

  4. Math

    Jeremy loves right triangles that have side length 1. In fact, he loves to combine them so that the hypotenuse of one becomes the leg of the next. If the longer leg of the first triangle is sqrt 11, what will be the hypotenuse of

You can view more similar questions or ask a new question.