How do I do this? For f(x, y), find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = 36 x + 6 y + xy

Question

For
f(x, y),
find all values of x and y such that
fx(x, y) = 0
and
fy(x, y) = 0
simultaneously.
f(x, y) =
36
x
+
6
y
+ xy

Answer 1

f(x,y) = 36x + 6y + xy

f_x(x,y) = 36 + y

f_y(x,y) = 6 + x

Note that f_x=0 and f_y=0 is a linear system in x and y. Solve the system:

x + 6 = 0

y + 36 = 0

You can finish from here.