find critical points and relative extrema, given an open region.
To find the critical point:
Find the partial derivative and equate to zero:
Differntiate f(x,y) with respect to x and equate to zero
Differntiate f(x,y) with respect to y and equate to zero
Hence, the critical point is (0,0)
Now we have to find the relative extrema.
Hence, by the
f(x,y) neither max. nor min at (0,0) which means (0,0) is saddle point.
use Green’s Theorem to find the counterclockwise circulation and outward flux for the field F and the curve C.
C: The square bounded by