5×9/10=4.5
9/10 1 8/10 2 7/10 3 6/10 4 5/10
---------------l--------------l---------------l----------------l----------------
5 5/10=4 1/2=4.5
has only one critical point at
. The function has Hessian
which is positive definite for all
, which means
attains a minimum at the critical point with a value of
.
To find the extrema (if any) along the boundary, parameterize it by
and
, with
. On the boundary, we have
Find the critical points along the boundary:
Respectively, plugging these values into
gives 11, 47, 43, and 47. We omit the first and third, as we can see the absolute extrema occur when
.
Now, solve for
for both cases:
so
has two absolute maxima at
with the same value of 47.
There is a app called Cymath it shows you how to do it and gives you the answer
When you dilate the image by 3, you would multiply each value by 3. Since it's center is around 0, we really don't have to worry about much else.
-1*3= -3
-2*3= -6
0*3= 0
The new set of points are (-3,-6,0)
I hope this helps!
~cupcake
