Simple maximization question very confused :s

In summary, the conversation discusses finding the maximum value of the function f(x) = x^2 subject to the constraint 0 ≤ x ≤ a, without using calculus. The conclusion is that the maximum value is a^2 and the value of x that maximizes the function is a. The reasoning behind this is that, for basic arithmetic, when x > y > 0, then x^2 > y^2, thus the maximum value is at a and it is equal to a^2.
  • #1
gajanan
1
0
Hey everybody!

My question is: Find the value of x that maximizes the following function and the maximum
value (a is constant): f(x) = x^2 subject to 0 ≤ x ≤ a.

It is supposed to be solved without calculus and I'm terrible confused! how would i go about solving this? wen i plot the curve i of course get half a parabola (positive half), and given the constraint 0 ≤ x ≤ a, the graph gets limited. I am confused what the answer to this question would be :s! would it be a^2 as the maximum value and a as the value of x that maximizes the function, or would it simply be 0 or not possible?!? any help would be appreciated greatly!
 
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  • #2
Basic arithmetic x > y > 0 => x2 > y2, so the max is at a and the max value is a2.
 

Related to Simple maximization question very confused :s

1. What is a simple maximization question?

A simple maximization question is a type of mathematical problem that involves finding the maximum value of a given function or set of values. It is commonly used in economics, computer science, and other fields to optimize a desired outcome.

2. How do I solve a simple maximization question?

The first step in solving a simple maximization question is to clearly define the objective function, which is the function or set of values that you want to maximize. Next, you will need to identify any constraints that must be met in order to find the maximum value. Then, you can use techniques such as differentiation or linear programming to solve the problem and find the maximum value.

3. What are some common applications of simple maximization questions?

Simple maximization questions are commonly used in economics, such as in determining the optimal production level for a company. They are also used in computer science for algorithms that aim to find the most efficient solution to a problem. In addition, simple maximization questions can be found in various fields such as engineering, finance, and operations research.

4. Can a simple maximization question have multiple solutions?

Yes, a simple maximization question can have multiple solutions. This can occur when there are multiple local maximum values for the objective function, or when the constraints allow for multiple optimal solutions. In some cases, the solutions may be equivalent, while in others they may differ in terms of efficiency or other factors.

5. How can I check if my solution to a simple maximization question is correct?

To check if your solution to a simple maximization question is correct, you can plug in the values found for the decision variables into the objective function and compare the result to the maximum value found. You can also verify that the solution satisfies all of the constraints. Additionally, it can be helpful to double check your calculations and problem-solving approach to ensure accuracy.

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