Question

Noah finds an expression for V(x) that gives the volume of an open-top box in cubic inches in terms of the length x in inches of the cutout squares used to make it. This is the graph Noah gets if he allows x to take on any value between -1 and 5. A.) What would be a more appropriate domain for Noah to use instead?B.) What is the appropriate maximun volume for his box?(I'm having a hard time figuring out a domain. I would really appreciate the help)

Answer 1

Answers:

A. 0 ≤ x ≤ 2.5

B. 15 cubic inches

Step-by-step explanation:

The domain is the set of values that x can take.

On the other hand, an appropriate domain is the set of values of x that have a sense in the problem. So, if x is the length in inches, a length of x = -1 doesn't have sense. Additionally, if for specific values of x, the volume is negative, these values of x shouldn't be in the domain.

Therefore, a more appropriate domain is: values between 0 and 2.5

0 ≤ x ≤ 2.5

Then, looking at the volumes that we get for values of x between 0 and 2.5, we can see that the maximum volume is when x = 1 and it is equal to 15 cubic inches.

Therefore, the appropriate maximum volume is 15 cubic inches.