Finding extrema of quadratic functions in two variables

[nonaks]

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!

 

[Mark44]

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.

 

[nonaks]

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.