pre-calculus

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An open box is made from a square piece of material 36 inches on a side by cutting equal squares from the corners and turning up the sides. Use your calculator to find the maximum volume this box can hold.

I got the equation 4x^3-36x^2+1296x = V

But when I put it in the calculator I don't know how to find the maximum value. How do I find the maximum value of a 3rd degree polynomial like this?

  • pre-calculus -

    Calculators can...
    Did you graph it?
    did you take the derivative of it, and solve that?

    I have no idea what you are doing with your calculator. I recommend graphing.

  • pre-calculus -

    I tried graphing but when I put it in I get a negatively shaped parabola (below the x-axis) and I don't know how to find the maximum value for a parabola like that.

  • pre-calculus -

    volume=b*b*h
    = (36-2x)^2 x
    = (1296-144x+4x^2)x

    I don't get the same equation as you

  • pre-calculus -

    That's the same exact equation but you took out an x.

  • pre-calculus -

    no, you had a 36 term.

  • pre-calculus -

    Oops, that was a typo. I tried taking 4x out and typed in 36x^2. That should be 144x^2. Aka, the same equation as yours.

  • pre-calculus -

    Can anybody figure out how to find the maximum value on this? -b/2a doesn't work either since it's not a 2nd degree polynomial.

  • pre-calculus -

    graphing y=4x^3-144x^2+1296x

    I get a clear maximum around x=5.7

  • pre-calculus -

    What are your window settings?

  • pre-calculus -

    x max 10
    y max 10000

  • pre-calculus -

    An open box is to be made from a flat piece of material 18 inches long and 5 inches wide by cutting equal squares of length xfrom the corners and folding up the sides.
    Write the volume Vof 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 box as an open interval in the form (a,b), then what is a=?
    a=
    and what is b=?
    b=

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