DAmon you equaled them to zero that is not rightt

Question

An open-topped box can be made from a rectangular sheet of aluminum,
an open-topped box can be made from a rectangular sheet of aluminum, with dimensions 40 cm by 25 cm, by cutting equal-sized squares from the four corners and folding up the sides.

Declare your variables and write a function to calculate the volume of a box that can be formed.

I figured out this part because the function would be f(x)=x(25-2x)(40-2x)

x being the height
25-2x being the width
40-2x being length

Then it asks what cut lengths to the nearest hundredth are acceptable if the volume of the box must be between 1512 and 2176cm^3.

So you would the write 1512<x(40-2x)(25-2x)<2176

how to you solve the inequality to get the x
PLEASE HELP THNX I HAVE A TEST TMR

Answer 1

I set them equal to 1512
and then to 2176

THEN
I subtracted 1512 from the first both sides
AND
I subtracted 2176 from the second both sides

PLEASE calm down and think

Answer 2

ya but they are inequalities
1512<x(40-2x)(25-2x)<2176

it does not equal 1512 it is bigger than it hence this (<)

Answer 3

so wouldnt it be
4x^3 - 130x^2 + 1000x - 1512 > 0 instead of equalling

Answer 4

I did the two equations at the limits and said look between them

Answer 5

go back to where Steve is helping you as well and look at the graphs. Watch out though, the third region makes the box higher than half the width so will not work.

Answer 6

If you are still stuck, look at the graphs Steve linked you to carefully and see three areas between the curves on the x axis. Those are values of x where your original function is between the limits. The last area on the right is not feasible because the width would be negative if the box were that high.