Find the max value of xy (done in a weird way)

In summary, the conversation discusses finding the maximum value of xy given that x and y satisfy the equation 4x+y=2. The conversation mentions using derivatives to solve this problem, but one person suggests using a different method which turns out to give the same answer. However, upon further discussion, it is determined that the suggested method is not logically sound and is likely just a coincidence.
  • #1
Andrax
117
0
find the max value of xy (done in a "weird" way)

Homework Statement


so our teacher assigned this homework in the last 10 minutes
we haven't read the function with 2 variables and I've never seen/used one
(things were just getting in my head since it's only 10 mins i don't know if I'm making a mistake)
suppose that x and y satisfie 4x+y=2
find the maximum value of xy
so this is done with deriviatives but i was thinking in using another way and it turned to be right , what I'm asking here is explaining why my method was right, anyway the answer is (1/4 , 1) this is how I've done it
f(x)=4x+y-2 must be eqUAL TO 0
f(xy)=4xy+y-2 this must be equal to 0( assumed that y is not changing i don't know )
anyway this leads to x=2-y/4y
replacing in 4x+y=2 we get y= 1 then x=1/4
now our teacher used derviatives to solve this
y=2-4x
xy=2x-4x^2 etc and he gets the exact same answer as me , i don't think this is a coincidence so please explain to me why this is right , when i asked him he mentioned two variable functions..
thanks everyone :)
 
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  • #2
Andrax said:

Homework Statement


so our teacher assigned this homework in the last 10 minutes
we haven't read the function with 2 variables and I've never seen/used one
(things were just getting in my head since it's only 10 mins i don't know if I'm making a mistake)
suppose that x and y satisfie 4x+y=2
find the maximum value of xy
so this is done with deriviatives but i was thinking in using another way and it turned to be right , what I'm asking here is explaining why my method was right, anyway the answer is (1/4 , 1) this is how I've done it
f(x)=4x+y-2 must be eqUAL TO 0
f(xy)=4xy+y-2 this must be equal to 0( assumed that y is not changing i don't know )
Where did 4xy + y - 2 come from? In particular, the 4xy part.

Edit: Now I see what you did, which was to substitute xy for x in the function definition. Even so, I'm not sure that what you did after that makes sense.
Andrax said:
anyway this leads to x=2-y/4y
What you wrote is x = 2 - (y/4 * y). Is that what you meant? Or did you mean x = (2 - y)/(4y)?
Andrax said:
replacing in 4x+y=2 we get y= 1 then x=1/4
now our teacher used derviatives to solve this
y=2-4x
xy=2x-4x^2 etc and he gets the exact same answer as me , i don't think this is a coincidence so please explain to me why this is right , when i asked him he mentioned two variable functions..
thanks everyone :)
 
Last edited:
  • #3
Yes it doesn't look logical anyway thanks
 
  • #4
Andrax said:

Homework Statement


so our teacher assigned this homework in the last 10 minutes
we haven't read the function with 2 variables and I've never seen/used one
(things were just getting in my head since it's only 10 mins i don't know if I'm making a mistake)
suppose that x and y satisfie 4x+y=2
find the maximum value of xy
so this is done with deriviatives but i was thinking in using another way and it turned to be right , what I'm asking here is explaining why my method was right, anyway the answer is (1/4 , 1) this is how I've done it
f(x)=4x+y-2 must be eqUAL TO 0
f(xy)=4xy+y-2 this must be equal to 0( assumed that y is not changing i don't know )
This is incorrect. Because 4x+ y- 2= 0 for all x and y, if x changes, y must also change. In particular, you cannot write "f(x)= 4x+ y- 2" because f depends upon values of both x and y.

anyway this leads to x=2-y/4y
replacing in 4x+y=2 we get y= 1 then x=1/4
now our teacher used derviatives to solve this
y=2-4x
xy=2x-4x^2 etc and he gets the exact same answer as me , i don't think this is a coincidence so please explain to me why this is right , when i asked him he mentioned two variable functions..
thanks everyone :)
Looks to me like shear coincidence. Your "method" is NOT valid.
 

Related to Find the max value of xy (done in a weird way)

1. What is the purpose of finding the max value of xy in a weird way?

The purpose of finding the max value of xy in a weird way is to explore different methods and approaches in solving a problem, which can lead to new discoveries and advancements in science.

2. What does "weird way" mean in this context?

In this context, "weird way" refers to a non-traditional or unconventional approach to finding the max value of xy. It may involve using unique techniques or thinking outside the box.

3. Can you provide an example of finding the max value of xy in a weird way?

One example of finding the max value of xy in a weird way is using a genetic algorithm, which mimics natural selection and evolves a solution over time. This approach may not be the most efficient, but it can lead to unexpected and sometimes optimal results.

4. How is finding the max value of xy in a weird way different from the traditional method?

The traditional method of finding the max value of xy may involve using calculus or other mathematical formulas. In contrast, finding it in a weird way allows for more creativity and experimentation, often using computer algorithms or simulations.

5. Is finding the max value of xy in a weird way necessary for scientific progress?

No, it is not necessary for scientific progress, but it can be a useful tool in exploring new ideas and pushing the boundaries of knowledge. It can also lead to unexpected insights and solutions, which can contribute to scientific progress in the long run.

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