a) Let f(x, y) = x³ + y³ – 3x² – 3y² – 9x. Find and classify all the critical points (whether they are points of local maxima, local minima, saddle points or neither of those. b) Does this function have global maximum and/or minimum on its domain R?? Compute them if it does. c) Do the same for the function f(x,y) = xª + y*. Try to classify even the critical points where the second derivative test does not apply.

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A: Given that  fxx=3x^2 and D(x,y)=4y-12  Points p(-1,4) and Q(4,2)  To find the which of the following…

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Q: (4) Let g(x, y) = xye¬²-y². (a) Find all critical points. (b) Classify the critical points found in…

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Q: 1. Consider the function f(x, y) = -3 +4xy – 2y² +3. (a) Find all critical points (b) Classify these…

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Q: 6. Let f(x, y) = x3 – xy+ y. Find the critical points off and determine if they are local minima,…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: f (x, y) = 5ye" – e5x – yð

A: for critical points equate the first derivative wrt x and y to zero.

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A: We have to find

Q: Given a function f ( x, y) = x3 + y3 + 3x2 -18y2 + 81y + 5 The function has four critical points…

A: The given function is fx,y=x3+y3+3x2-18y2+81y+5. Obtain the critical points as follows:…

Q: Let f(x, y) = y³ + x² – 3y Prove that the Critical points are (0,1), (0, – 1),

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Q: Consider the Freudenstein and Roth test function f(x)= f;(x)² + f2(x)², xER?, where fi(x) =-13+x1…

A: (i)

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Q: 8. Determine if the critical point (0,0) of f(x,y) =x³+2xy² – y4 +x² + 3xy+y² +10 is a local…

A: f(x,y) = x3 + 2xy2 - y4 + x2 + 3xy + y2 + 10 => fx = 3x2 + 2y2 + 2x + 3y      fxx = 6x + 2…

Q: give the critical points of f(x,y) = 2x^3 + xy^2 + 5x^2 + y^2. classify each as a local minimum,…

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Q: 6. Find all critical points of f(x,y) = 2yt + x2 – 6xy and classify each critical point as a local…

A: Answer

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Q: 8. Find the local minimum and the local maximum and saddle points of f (x, y)= x² + y' - 3x² - 3 y²…

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Q: Let f(x) = 6x²(x – 1) + 10. %3D Find the critical points c that correspond to local minima.

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Q: Use Lagrange multipliers to find the critical points and the relative extrema. f(x,y,z) = x² + y² +…

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Q: Consider the function f(x, y) = x³y+ 9x² – y, defined on the set D = {(x, y) | x² + y² < 100}. (a)…

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Q: Find all the critical points of the function and determine at each one whether there is a local…

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Q: Construct a suitable Lyapunov function of the form ax? + cy², where a and c are to be determined,…

A: Since you have asked multiple question, according to our guidelines we will solve the first question…

Q: Consider (x, y, z) = x² + y² + z² + 2xyz. Show that (0,0,0) and (-1, 1, 1) are both critical points.…

A: Here we solve the given calculus problem.

Q: 7. Use the Method of Lagrange Multiplier to find the critical points of the function f(x,y, z) = 2x²…

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Q: 1. Let f(x, y) = x³ – 3.xy + y3. Find all critical points of f and at each critical point, use the…

A: We have to find the saddle point, relative maxima or minima of f(x,y).

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Q: 1 5. Define f(x, y) = x³ + y? – 2xy – 3x. (a) Find all the critical points of f. (b) Determine…

A: The solution is given below:

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Q: 1. Let f(x, y) = y³ + x³ - 2y² - 3x + 30y. (a) Find all the critical points of f. (b) Determine…

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Q: Let g(x,y) = x³ – 6x² – y* + 5. Find and classify the critical point(s) of g.

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Q: 2. Let f(r, y) = x² – 2xy + 2y² – x + 3. (a) Determine all the critical points of f. (b) Determine…

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Q: Let f(x, y) = 2x³ – 3x²y – 12x? – 3y². - Then the critical point (-4,-8) of f is: O a local maximum…

A: We need to choose correct option.

Q: Given a function f(x, y) = x° + y° + 3x² – 18y + 81y + 5 - The function has four critical points in…

A: Consider the given function as fx,y=x3+y3+3x2-18y2+81y+5

Q: 1. Let f(x, y) = y³ + x³ - 2/1y²-3x+30y. (a) Find all the critical points of f. (b) Determine…

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Q: (b) Given that one of the critical points for the function f(x, y) = xy–*y-xy' is (0.4, V0.2). i.…

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Q: 5. Let f(x, y) = x² + y? – xy + x. Find the critical point of f and determine if it is a local…

A: We will find the critical point for the given function.Also we will find that given function is…

Q: 16 Let f(x, y) = x² + +y² 16 -. Classify all critical points of this function as being local…

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