Setting Up the Domain for Maxima/Minima Word Problems

  • Thread starter frozonecom
  • Start date
  • Tags
    Domain
In summary, the conversation discusses setting up the domain of a function that models a word problem involving creating a box from a metal sheet. The volume equation is given, but there is confusion about which interval to use for the domain. The options of [0,6] and (0,6) are discussed, with the book using (0,6) and the speaker questioning why. The issue of local minima is also mentioned.
  • #1
frozonecom
63
0
Good day everyone.
I'm confused about how I SHOULD set up the domain of my function that models the word problem.

Suppose I have a word problem that goes like this:
A square box with no top is to be made by cutting congruent squares from the four corners of a square metal sheet and then folding up the resulting flaps. If the length of a side of the metal sheet is 12 in., how should the square be cut in order to make a box with the largest possible volume?

Okay, so my volume equation is V(x)=(12-2x)(12-2x)(x)

I know how to solve this kind of equation but, how do I know what interval I should consider?
Should I use [0,6] or (0,6)?
Can anyone give tips on how to know which one?
My book used (0,6) but I don't really understand why. I know its meaningless to say you cut the corners by 0 cm^2, since you didn't really cut anything. Also 6cm^2, since by then none will be left for the open-top box. But how do I really know the domain of my function?

I'm really confused. Help would be really appreciated.
 
Physics news on Phys.org
  • #2
[0,6] will work as well. You just get the issue that 0 and 6 might be local minima of the volume, and appear as option in the solution (as the derivative is zero there), even if you know already that they cannot be the solution.
 

1. How do I determine the domain for a maxima/minima word problem?

To determine the domain for a maxima/minima word problem, you need to carefully read the problem and identify any restrictions on the variables. These restrictions may be in the form of specific values that the variables cannot take, or they may be implied by the context of the problem. Once you have identified the restrictions, you can determine the range of values that the variables can take, which will be your domain.

2. Can the domain for a maxima/minima word problem be negative numbers?

Yes, the domain for a maxima/minima word problem can include negative numbers. It all depends on the specific problem and the restrictions placed on the variables. It is important to carefully read the problem and identify any restrictions before determining the domain.

3. How do I graph the domain for a maxima/minima word problem?

To graph the domain for a maxima/minima word problem, you can plot the values on a number line. If the domain is continuous (i.e. it includes all values between two specific numbers), you can draw a line segment connecting the two points on the number line. If the domain consists of specific values, you can mark those values on the number line with dots. This will give you a visual representation of the domain.

4. What is the difference between the domain and the range in a maxima/minima word problem?

The domain refers to the set of values that the independent variable can take in a function, while the range refers to the set of values that the dependent variable can take. In a maxima/minima word problem, the domain will typically involve values that can be manipulated or changed, while the range will involve values that are dependent on the domain and may represent a maximum or minimum value.

5. Can the domain for a maxima/minima word problem change over time?

Yes, the domain for a maxima/minima word problem can change over time. This may occur if the restrictions on the variables change in the problem, or if the problem involves a real-life situation that is subject to change. It is important to carefully read the problem and identify any changes in the domain as you solve the problem.

Similar threads

MHB Dimension of the cut-out squares that result in largest possible side area
    • General Math
Replies
3
Views
3K
How can you maximize the volume of a box made from a rectangular sheet?
    • Calculus
Replies
1
Views
1K
Finding domain for when composite function is continuous
    • Calculus and Beyond Homework Help
Replies
3
Views
833
MHB Finding the domain of this function.
    • General Math
Replies
5
Views
953
MHB Maximizing Volume of a 5-Sided Box w/ Cutout Corners
    • Calculus
Replies
1
Views
1K
MHB Troubleshooting a Trigonometric Integral: Algebra and Solutions
    • Calculus
Replies
4
Views
2K
I am having trouble with 2 volume and a profit problems?
    • Calculus
Replies
3
Views
2K
I Motivation for Fourier series/transform
    • Calculus
Replies
8
Views
4K
Surface integrals/Surface areas of arbitrary domain regions
    • Calculus
Replies
3
Views
1K
Optimization problems involving non-compact domains
    • Calculus
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top