Calculus

posted by .

A manufacturer constructs open boxes from sheets of cardboard that are 6 inches square by cutting small squares from the corners and folding up the sides. The Research and Development Department asks you to determine the size of the square that produces a box of greatest volume. Proceed as follows. Let x be the length of a side of the square to be cut and V be the volume of the resulting box. Show that V = x(6-2x)^2 (sketched it already.)

Are there any restrictions on the value of x? Explain.

Estimate the largest volume.

  • Calculus -

    This is a continuation of the question I answered for you earlier.
    Since you titled it "Calculus" you should be able to finish it.
    1. expand and simplify the expression for V
    2. differentiate, you will have a quadratic
    3. solve that quadratic by setting it equal to zero for a max of V
    4. sub the value you found in 3. into the original volume equation

    for the restriction, all you have to do is look at the equation for V
    V of course has to be positive.
    so x > 0 and x < 3 or else the base side values make no sense.
    restriction on x : 0 < x < 3

  • Calculus -

    hjbsxn

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math Wrod Problem

    1. A long strip of copper 8 inches wide is to be made into a rain gutter by turning up the sides to form a trough with a rectangular cross section. Find the dimentions of the cross-section if the carrying capacity of the trough is …
  2. algebra

    Open-top box. Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what …
  3. Calculus

    A SHEET OF CARDBOARD 180 INCHES SQUARE IS USED to make an open box by cutting squares of equal size from the corners and folding up the sides, what size squares should be cut to obtain a box with the largest possible volume?
  4. calculus

    7. A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 40 cm by 60 cm by cutting equal squares from the four corners and turning up the sides. Find the length of the side of the …
  5. Calculus

    A manufacturer constructs open boxes from sheets of cardboard that are 6 inches square by cutting small squares from the corners and folding up the sides. The Research and Development Department asks you to determine the size of the …
  6. math

    a rectangular sheet of cardboard 4m by 2m is used to make an open box by cutting squares of equal size from the four corners and folding up the sides.what size squares should be cut to obtain the largest possible volume?
  7. Math

    A cardboard manufacturer wishes to make open boxes from square pieces of cardboard of side 12 in. by cutting equal squares from the four corners and turning up the sides. Let x inches be the length of the side of the the square to …
  8. Calculus

    A square sheet of cardboard with a side 16 inches is used to make an open box by cutting squares of equal size from the four corners and folding up the sides. What size squares should be cut from the corners to obtain a box with largest …
  9. Calc

    A cardboard box manufacturer makes open boxes from rectangular pieces of cardboard of size 30cm by 40cm by cutting squares from the four corners and turning up the sides. A) find a mathematical model expressing the volume of the box …
  10. Calculas

    an open box is to be made from a square piece of cardboard whose sides are 19 inches long,by cutting squares of equal size from the corners and bending up the sides. Determine the size of the aquare that is to be cut out so that the …

More Similar Questions