Answer:
Explanation:
Consider that F (any function) <0 .
u(x,y) is a coontinuous function in the closed interval or region R.
Let us consider a point (p,q) that is inside the region and it is a maximum point.
Then it should be must
uxx (p,q) <0 where uxx means double differentiation
and uy(p,q) >0
Since ux(p,q) = 0 = uy(p,q) where ux and uy means single differentiation with respect to x and y respectively.
Say, Maximum limits of the region is T
therefore q<T
then uy (p,q) = 0 if q<T
if q = T then
point (p,q) = (p,T) will be on the boundary of R then we claim that
uy(p,q) >0
Similarly for the minimum also it will work
