An open box of maximum volume is to be made from a square piece of material 24 cm on a side by cutting equal squares from the co
rners and turning up the sides (see figure).
a. Write volume V as a function of x, the length of the corner squares.
b. What is the domain of the function?
1 answer:
Answer:
V = x(24 - x)^2 cm^3.
Domain = (0, 24).
Step-by-step explanation:
a. Let the lengths of the sides of the squares be x cm.
Then the lengths of the sides of the base of the box will be (24 - 2x) cm.
The height of the box will be x cm.
So the required volume
= height * area of base
So V = x(24 - x)^2
b. The domain of this function is (0, 24).
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