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.

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

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

I don't get the same equation as you

Answer 4

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

Answer 5

no, you had a 36 term.

Answer 6

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.

Answer 7

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.

Answer 8

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

I get a clear maximum around x=5.7

Answer 9

What are your window settings?

Answer 10

x max 10
y max 10000

Answer 11

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=