how would you find the exact extreme values of this function?

f(x,y) = (x-5)^(2) + (y-1)^(2) + 36

x is less than or equal to 19
y is less than or equal to 13

Question

how would you find the exact extreme values of this function?

f(x,y) = (x-5)^(2) + (y-1)^(2) + 36

x is less than or equal to 19
y is less than or equal to 13

zepdrix · Answer

Mmmmmm I don't remember.. I think for multivalued functions it's when,$$\Large\bf\sf f_x=0,\qquad\text{and}\qquad f_y=0$$right? +_+

anonymous · Answer

just differentiate it, it is implicit curve..
then you would find x=5 and y is complex number

anonymous · Answer

check Fx = 0 and Fy = 0, and also check the boundaries.

anonymous · Answer

so how would you know the max and min?

anonymous · Answer

Irrelevant: I've just come back after a few weeks, and LaTeX is back.
YES!

anonymous · Answer

??

whpalmer4 · Answer

So same deal as with our other problem:
Expand $$f(x,y) = x^2-10x+y^2-2y+62$$Take partial derivatives and set equal to 0
$$2x-10 = 0$$$$x=5$$$$2y-2=0$$$$y=1$$
Extreme value is $f(5,1) = (5)^2-10(5)+(1)^2-2(1)+62 = 36 $

Contour plot attached