Proving the Converse of the Parallelogram Side Theorem
1 answer:
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Answer:
A(-1,0) is a local maximum point.
B(-1,0) is a saddle point
C(3,0) is a saddle point
D(3,2) is a local minimum point.
Step-by-step explanation:
The given function is
The first partial derivative with respect to x is
The first partial derivative with respect to y is
We now set each equation to zero to obtain the system of equations;
Solving the two equations simultaneously, gives;
and
The critical points are
A(-1,0), B(-1,2),C(3,0),and D(3,2).
Now, we need to calculate the discriminant,
But, we would have to calculate the second partial derivatives first.
At A(-1,0),
and
Hence A(-1,0) is a local maximum point.
See graph
At B(-1,2);
Hence, B(-1,0) is neither a local maximum or a local minimum point.
This is a saddle point.
At C(3,0)
Hence, C(3,0) is neither a local minimum or maximum point. It is a saddle point.
At D(3,2),
and
Hence D(3,2) is a local minimum point.
See graph in attachment.
