Solution:
There is no saddle point (DNE). However, there is local maximum at (1, 1/2) for the given function.
Explanation:
we have function of two variables f(x,y)= 9-2x+4y-x^2-4y^2
we will find the values by partial derivative with respect to x,y,xy
= -2 -2x
= 4 -8y
to find the saddle point we should first find the critical points so equate
-2 -2x=0 and 4 -8y=0
we get x= 1 and y =1/2 so, critical points are (1,1/2)
to find local maximum or minimum we have to find ,
and
formula is *
-
=0
= -2
= -8
=0
putting values in formula
(-2)*(-8) -0 =16 > 0, and < 0 and
<0
so, here we have local maximum
we have no saddle point for this function by using the same formula we used to find extrema.
