Good dayCan anyone pls teach me how to find the extrema of this

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In summary, the person is asking for help in finding the extrema of a general second degree polynomial function. They are unsure of how to approach this type of problem and are looking for guidance. The recommended method is to find the two first partials and set them to zero, then use a test to categorize the critical points. The person has not learned this topic from a book and it is not covered in their syllabus, but they will continue to try and solve it.
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nonaks
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Good day!

Can anyone pls teach me how to find the extrema of this function (general second degree polynomial function): f(x,y)=x^2+4xy+4y^2-2x+3y+6. actually, my problem is i don't know how to find the extrema of functions of this form f(x,y)=ax^2+bxy+cy^2+dx+ey+f.

Your help will be highly appreciated.

Thanks!
 
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  • #2


Find the two first partials and set them to zero. The critical points (x, y) are those for which both first partials are zero. There's a test for categorizing the critical points that involves the 2nd partials.

Your textbook should have examples showing how this is done.
 
  • #3


Thank you for the quick reply sir. I haven't read this topic from a book before. It is not covered in our syllabus. This is an open problem given to me by my professor.

I'll read more and will post again if i can't figure out the mess.
 

1. What is an extremum?

An extremum is a maximum or minimum value of a mathematical function.

2. Why is it important to find extrema?

Finding extrema helps in understanding the behavior of a function and can be used to optimize a system or solve real-world problems.

3. How do you find extrema of a function?

To find extrema, you need to take the derivative of the function and set it equal to zero. Then, solve for the variable to find the critical points. Finally, plug in the critical points into the original function to determine the type of extrema.

4. What is the difference between a local and global extrema?

A local extrema is the maximum or minimum value of a function within a specific interval, whereas a global extrema is the maximum or minimum value of a function over its entire domain.

5. Can extrema occur at more than one point?

Yes, a function can have multiple extrema, both local and global, depending on its shape and behavior.

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