You construct an open box from a square piece of material, 18 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides. (see figure) (a)Write a function V that represents the volume of the box. (b)Determine the domain of the function V.(Enter your answer using interval notation) (c)Use a graphing utility to construct a table that shows the box heights x and the corresponding volumes V(x). Use the table to estimate a range of dimensions within which the maximum volume is produced.
You construct an open box from a square piece of material, 18 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides. (see figure)
(a)Write a function V that represents the volume of the box.
(b)Determine the domain of the function V.(Enter your answer using interval notation)
(c)Use a graphing utility to construct a table that shows the box heights x and the corresponding volumes V(x). Use the table to estimate a range of dimensions within which the maximum volume is produced.
(d)Use the graphing utility to graph V.
In the given question there is a square piece of 18 inches on a side, is given and an open box is constructed from it by cutting equal squares with sides of length x from the corners and turning up the sides.
We have to calculate its function of volume.
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