Consider the function v=g(x), where g(x) =x(6-2x)(8-2x), with x being the length of a cutout in cm and v being the volume of an open box in cm³, where x must between 0 and 3 cm. determine the maximum volume of the open box in cm³. round your answer to two decimal places. also, indicate or show what process you used to obtain this answer. (hint: graphing)

The maximum volume of the open box is 24.26 cm³

Step-by-step explanation:

The volume of the box is given as , where and .

Expand the function to obtain:

Differentiate  wrt  x to obtain:

To find the point where the maximum value occurs, we solve

Discard x=3.54 because it is not within the given domain.

Apply the second derivative test to confirm the maximum critical point.

,

This means the maximum volume occurs at .

Substitute into to get the maximum volume.

The maximum volume of the open box is 24.26 cm³

See attachment for graph.

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.

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step-by-step explanation: