Find f f, and f,, and evaluate each at the given point. ху f(x, y, z) = (2, 1, –1) %3D x + y + z fx(X, y, z) = ,(x, y. z) = %3D f,(x, Y, z) = %3D f,(2, 1, -1) = fy(2, 1, -1) = f(2, 1, –1) = %3D

Q: 1. ( A) Find the linearization of the function at the given point. f (x, y) = (x + y + 1)², at (2,…

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Q: x+y If Z = x.n. f (***), then show that: X. Zx + y.Zy = z

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Q: 3. Let f(r, y) = y²x – yx² + xy. Find all critical points of f.

A: We have to determine critical points of f

Q: (a) Find and classify the critical points of f(x, y) = xye-(2²+v*)/2, (b) Find and classify the…

A: (a) Given f (x,y,z)=xye-x2+y2/2  ∂f∂x=(1-x2)ye-x2+y2/2 ∂f∂y=(1-y2)xe-x2+y2/2

Q: Find the local max/min value(s) and saddle points of f(x, y) = x^4+y^4−4xy+1.

A: Given: f(x,y)=x4+y4-4xy+1 To find the local maximum, local minimum and saddle points of f(x,y). The…

Q: Find all the local maxima, local minima, and saddle points of the functions f(r, y) = In(x+ y) + x²…

A: To find the local maxima, local minima, and saddle points of the function given.

Q: Exercise 2: Suppose that the joint pdf of (X, Y)' is fx.y(r,y) = c(r + y), if r € 0,1, 2,3 %3D and y…

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Q: 1 If f(x, y,z)= ôf then 2у - х —z a. 2 (2y-x-2) b. 1 (2y -x-2)2 с. -1 (2y –x-2) d. 1 (2y–x-2)

A: It is derivative problem.

Q: A person has a direct utility function as follows: u(x, x,) a) Find the expenditure function and…

A: Given, direct utility function: ux1, x2=x1x21+x2 We need to find the expenditure function and…

Q: If f(x,y,z) = e(x+y+z) then find f +f,+f; %3D a. fx+fy+f, = (x+y+z)e(x+y+z) O b. None ° C. fx+fy+f,…

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Q: 1. A) Find the linearization of the function at the given point. f (x, y) = 2 + x In (4 – xy), at…

A: (NOTE- These are two completely different questions, only required to do the first one. Please post…

Q: Which of the following is the orthogonal trajectories of the family of cissoids y² = ? a- y² = C(x +…

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Q: a) Find all four critical points for the function f(x, y) = y³ + x²y + 9y² + 2x².

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Q: Find all the local maxima, local minima, and saddle points of the functions in Exercises 1–4. 1.…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 21. Find div(F), where F(x, y, z) = xyzªi+x²zªj +4x²yz³k. a) -4xyz³+xz4 b) x²y+xz4 c) yz + 3x²yz² d)…

A: Topic = Algebra Correct option = d

Q: The number of defects on the front side (X) of a wooden panel and the number of defects  on the rear…

A: Here, fXY (x, y) = c(x+y) Joint Distribution of X and Y can be formulated as: X\Y 1 2 3 Total of…

Q: (x* + y° ) In (x² + y* ). (x,y)= (0,0) f(x, y) = k +1, (x, y) = (0,0)

A: If f is continuous then lim (x, y) tends to (0, 0) =k+1 And using l hospital rule.

Q: Find the critical points for f(x,y) = x² + xy + y? - 3x + 2. O A. (-2,- 1) О В. (-2,1) О С. (2,1) O…

A: We have to find the critical point of given function.

Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

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Q: Find the average of the given function on the given interval. (a) y = cos x, [0, 3π/2] (b) y = x² +…

A: a) y=cos x, 0, 3π2b) y=x2+x+1, 0,1

Q: The function f(x) = Ei-1 Cix;| is piecewise linear and convex. True O False

A: Step:- 1 Convex piece-wise Linear: - A function f: ℝn→ℝis a convex piece-wise linear if there exist…

Q: a) Find the maximum percentage error in z if the percentage error in x is 1% and y is 2% given that…

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Q: 10. Find the local maximum and minimum values and saddle point(s) of the function f(x, y) = x3 –…

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Q: Find the linearization L(x) of the function at a. f(x) = rad(x),    a = 25

A: Given,

Q: z= f(x, y) = 10x- 10y+xy-x +y Verilen fonksiyonun eyer noktası hangisidir? (Which one is the saddle…

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Q: Find the local max and local min and saddle points of F(x,y)= 2x^2+y^4-4xy

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Q: (I) The critical points of the function f(x, y) = 3y² – 2y³ – 3x² + 6xy are: (a) (0,0), (2,1) (b)…

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Q: Thank you!

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Q: Find and classify the critical points of f(r, y) = 2y²x- ya? + 4yx.

A: Here we have to find and classify the critical points of f(x,y) = 2y2x - yx2 +4yx .

Q: O Let f : A - B be an injection, and X, Y CA. Show that f(Xn Y) = f(X)nf(Y). |

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Q: If (a,ß) is a saddle point of the function f(x,y)=20y²-y³+3x2-6xy, then a+ß=

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Q: Calculate fw(-1, 2, 0, –1) where f(x, y, z, w) = xy²z – xw² – e2a²-v²-²+2w²

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Q: 5. Determine whether the functions y, and y2 are linearly dependent on the interval (0,1). Yi = 1+…

A: Linearly independent of the function. Using Wronskian

Q: The productivity of a certain country with the utilization of x units of labor and y units of…

A: It is given that,  f(x,y)=100x0.72y0.28

Q: Let f(x, y) = x³ + y3 – 9xy + 27, then (3,3) is saddle point. True False

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Q: (ii) Suppose z = f(x, y), where x = g(s, t), y = h(s, t), g(1,2) = 3, gs (1, 2) = −1, gt(1, 2) = 4,…

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Q: Find the local min and max values and saddle points of the function f(x,y)= x + y3 + xy

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Q: Find and classify all the critical points of f(x,y)=−3xy(15−x−y)

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Q: Find and classify the critical points of f(x, y) = 2rye¬x²-y°.

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Q: Determine E (X) and V (X) y f(x, y) -1.0 -2 1/3 -0.5 -1 1/6 0.5 1 1/6 1.0 2 1/3

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Q: If V f(x, y) = (x² - 1,√y-1), then f have two critical points (1, 1) and (-1, 1). Select one: O True…

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Q: Find div F if F(x, y, z) = (x² + y)i + z²j + (eY - z) k.

A: Our Aim is to find the value of div F if F(x,y,z)=x2+y i +z2 j+ey-zk -(i)Let  F(x,y,z)=x2+y i +z2…

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

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Q: Which of these critical points is the saddle point of the equation: f (r, y) = 4 + x³ + y' – 3zy A.…

A: Let us find the saddle point of the given equation in the next steps.

Q: f(x) = ³√x, a=27

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Q: O Find all local max, local min, and saddle points of f (x, y) = xy – x²y – xy?

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Q: If f(x, y) = 3x³ + y² - 9x + 4y, then the saddle point is (1, 2) O None of them O (1,-2) O (-1,-2) O…

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Q: Data sets A and B are dependent. Find the critical value, to, to test the claim that Ha = 0. Use a =…

A: Given that Sample size n = 5 Level of significance = 0.05

Q: 15. f(x, y, z) = xy + yz + zx, Po(1,-1, 2),u= 3i + 6j - 2k

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