Hi, Please help me find: V, a, and b. Ty

An open box is to be made from a flat piece of material 8 inches long and 2 inches wide by cutting equal squares of length x from the corners and folding up the sides.
Write the volume V of the box as a function of x. Leave it as a product of factors, do not multiply out the factors.
V= ?

If we write the domain of the volume of the box as an open interval in the form (a,b), then what is a=?
a= ?
and what is b=?

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  1. MMMhhh?
    Both I and bobpursley answered you .

    Why are you reposting?

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    posted by Reiny
  2. L = 8 - 2x
    W = 2 - 2x

    V = L W x
    V = (8-2x)(2-2x)x
    V = 4(4-x)(1-x)x
    V = 4 x (4 -5x + x^2)
    V/4 = x^3 - 5x^2 + 4x
    If x is > 1 that is impossible because the width will be negative
    if x is 0, our volume is 0
    I wonder where V is maximum?
    where is derivative = 0?
    f' = 3 x^2 -10 x + 4
    that is 0 when
    x = [ 10 +/- sqrt(100 - 48)]/6
    x = [ 10 +/- 7.21]/6
    x = .465 or 2.88
    2.88 is outside of our domain or x so
    max V when x = .465
    so domain of V is from 0 to V(.465)=3.52

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    posted by Damon
  3. by the way, I would call that the range of V
    the domain of x is 0 to 1

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    posted by Damon

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