SOLUTION: A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. The graph below shows how the volume of the box in cubic inches, V, is relate

Question 1122302: A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. The graph below shows how the volume of the box in cubic inches, V, is related to the length of the side of the square cutout in inches, x.
a. a. The point (0.25,13.813) is on the graph. This means that when the volume of the box is _____ . Cubic inches when the cutout length is _____ inches.
b. When the cutout length is 2 inches, the volume of the box is 30 cubic inches. This means that the point ____is on the graph above.
c. Suppose the largest possible cutout length is 3.5 inches. Over what interval of x does the volume of the box decrease as the cutout length gets larger? (Enter your answer as an interval.)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

I'll tell you this much: Every point on the graph has the following form:

(a cut-out length, the volume of the box corresponding to that cut-out length)

in other words:

If you have a cut-out length of zero, then you have a zero volume box. If 3.5 inches is the maximum, it is the maximum because if you cut out that much you will also have a zero volume box. So the graph starts a volume zero when x = 0 and increases to some point and then begins to decrease until x = 3.5 at which point you no longer have a box. Since you didn't provide the dimensions of the original piece of paper, except to imply that the short dimension is 7 inches, no one can help you find that point where the volume ceases to increase and starts to decrease.

John

My calculator said it, I believe it, that settles it

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