You plan to construct an open box from a square piece of material, 18 centimeter

Question

You plan to construct an open box from a square piece of material, 18 centimeters on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure). 18-2x (a) Write a function V that represents the volume of the box +324r (b) Detemine the domain of the function V. (Enter your answer using interval notation.) (0,00) (c) use a graphing utility to construct a table that shows the box heights x and the corresponding volumes x) x, em V(x), cm3 256 4 400 5 320 216 112 Use the table to estimate a range of dimensions within which the maximum volume is produced. The x-value is between 1 cm and 4 cm. O The x-value is between 4 cm and 6 cm The x-value is between 6 cm and 7 cm.

Explanation / Answer

The domain is (0,9)

Here it is mentioned that length is 18-2x

As x goes on increasing length goes on decreasing

Length cannot be zero or negative

Hence domain x belongs to (0,9)

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