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calculus (PRE)

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This may be simple, but I'm not getting it. An open box of maximum volume is to be made from a square piece of material, 24cm on a side, by cutting equal squares from the corners and turning up the sides. The table for it is:
Height(x) Volume(V)
1 484
2 800
3 972
4 1024
5 960
6 864
If volume,V, is a function of x write the function and its domain.

  • calculus (PRE) -

    The table should be:
    1, 484
    2, 800
    3, 972
    4, 1024
    5, 960
    6, 864
    Sorry!

  • calculus (PRE) -

    volume= x^3 domain is 0<x<24cm

  • calculus (PRE) -

    height x
    length = 24 - 2x
    width = 24 - 2x

    volume = x(24-2x)(24-2x)
    v = x(576 - 96 x + 4 x^2)
    v = 4 x^3 -96 x^2 + 576 x

    now x may not be negative
    x may not be equal to or greater than 12 or there is no box bottom left
    so
    0 < x <12

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