Suppose f(x, y) = (x – y)(16 – ry). Answer the following. Each answer should be a list of points (a, b, c) separated by commas, or, if there are no points, the answer should be NONE.1. Find the local maxima of f.Answer:2. Find the local minima of f.Answer:3. Find the saddle points of f.Answer:

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Asked Dec 19, 2019
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Suppose f(x, y) = (x – y)(16 – ry). Answer the following. Each answer should be a list of points (a, b, c) separated by commas, or, if there are no points, the answer should be NONE.
1. Find the local maxima of f.
Answer:
2. Find the local minima of f.
Answer:
3. Find the saddle points of f.
Answer:
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Suppose f(x, y) = (x – y)(16 – ry). Answer the following. Each answer should be a list of points (a, b, c) separated by commas, or, if there are no points, the answer should be NONE. 1. Find the local maxima of f. Answer: 2. Find the local minima of f. Answer: 3. Find the saddle points of f. Answer:

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Expert Answer

Step 1

Given, two variable function

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S (x, y)= (x- y)(16– xy) on simplify ing , f (x, y)=x (16 – xy)-y(16– xy) f (x, y)=16x – x*y -16y + xy

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Step 2

In order to find local minima, local maxima and saddle point, differentiate partial and find the critical points and differentiate twice to classify.

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D(a,b) = f. (a,b)· f,» (a,b)- (f, (a,b))* D < 0 → Saddle point (a,b) D > 0 and f. (a,b) > 0 → local minima (a, b) D > 0 and f. (a,b) < 0 → local maxima (a, b) xX

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Step 3

Now, partial diffe...

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(x,y) = (16x – x'y-16y + xy*) (16x – x²y –16y + xy²) * (x,y)= Ôx f. (x, y)=16 – 2xy + y² ..(1) (x,y)=(16x –x'y – 16y + xy*) ây f, (x, y)= -x² - 16+2.xy -(2)

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