Let f(x, y) = 8+ 76xy+38x2 + 240y + . Find and classify the critical points of f.

Q: Find and classify all critical points of f (x, y)=x*+y*_4xy+1.

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Q: Prove that f (x, y) = (x + 2y)e*y has „no critical points.

A: Consider fx,y=x+2yexy. The critical points of two variable function exist at the points where both…

Q: Let f(x, y) = - 4xy² – 2x² + 8y². Find and classify the critical points of f.

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Q: Let f (x, y) = 2x3 + x2y - y2. Compute d2f/dx2, d2f/dy2, and d2f/dxdy at (x, y) = (1, 2).

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Q: Let f(x, y) = 3x² – x – 3y + 5y2 – 10xy. - - - List the critical point:

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Q: Let z = f(x, y) = 5x – x³ + 2xy – y². - Find and classify all the critical point(s) of this…

A: Differentiate the function fx,y=5x-x3+2xy-y2 partially with respect to x and y, to obtain fx and fy.…

Q: Find and classify the critical points of f(x, y) = 6xy – 4x³ – 3y?

A: According to our guidelines, we can answer only one question or three subparts of a question. other…

Q: Let f(x,y)=-x³+4xy-2y²+1; find the critical points of f and test them using D=D(x,y).

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Q: Let f(x,y) = x² – 8x + 2y² + 4y + 7. a. Find and classify all critical points of f.

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Q: Consider the R² – R function f defined by f (1, y) = 2² – 6x +3y² - . (a) Find all the critical…

A: For critical points we need to find first order partial derivatives of given function and substitute…

Q: Find and classify the critical points of the function f(x, y) = 4x²y - 2x - y².

A: We need to determine and classify the critical points of the function: f(x, y)=4x2y-2x-y2.

Q: Let f(x) 18xe 18 %3D (a) f'(x) : (b) Solve f'(x) 0 to determine the critical values of f.

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Q: Find the best linear approximation to f(x) = x² on the interval [0, 2].

A: Here we use Taylor's approximation.

Q: Determine the linear approximation of f(x) = x' at x = 1. О а. уз- 1 х-0 О Б. у3 1x +0 O c. Not in…

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Q: 3. Consider f : R2 → R defined by f(x,y) = y³ + 3x²y – 6x² – 6y? + 2. - (a) Determine the critical…

A: The given function is: f(x,y)=y3+3x2y-6x2-6y2+2

Q: Find and classify all critical points for the function f(x, y) = x + y – 4xy + 2 %3D

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Q: Find the critical point of the function: f(x, y) = 4x2 + 2y2 − xy + x

A: we have given a function f(x, y)  We have to find the critical point

Q: Let f (x, y) = x³ + y? – 4xy + 3x + 2y + 5. Find and classify all critical points of f.

A: *concept:- maxima and minima in partial derivatives.

Q: Let f(x, y) = 2x² + 2xy+ y² – 6x + 2y be given. Find and classify critical points of the given…

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Q: Find and classify the critical points of the function f(x, y) = x²y+ 4xy – 2y².

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Q: Let f (x, y) = y^2x − yx^2 + xy.  (a) Show that the critical points (x, y) satisfy the equations y(y…

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Q: The function f(x, y) = 2xy + y²x + 11 has %3D two critical points. Select one: O True O False

A: As per our guideline of multiple questions are posted we are supposed to answer the first one.  Here…

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: Find the local linear approximation L (x) of the function f(x) = 5 – x² at =2.

A: To find the linear approximation of given function.

Q: Find and classify all critical points of f(x,y)%3Dx'+y-4xy+1.

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Q: Find the linearization of the function f (x) = x° at z = 1.

A: Given, f(x)=x6

Q: Find all critical points of f and use the second partial derivative test to determine if there exist…

A: find critical points by putting fx and fy = 0

Q: Find and classify all the critical points of f(x, y) = x³ - y³ - 8xy.

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Q: Let f(r, y) = 2x² – 8y + 112. (a) Find and classify the critical points of f(r, y).

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Find the critical point (xo, yo) of the function f(x, y) = 2x2 + 2xy + y? + 2x – 3.

A: Consider both the image for the solution.

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

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Q: For the function f(x,y) = –x² – xy – y² + 3x + 3y + 4, find and classify all critical points.

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Q: Disccus the hatural of the Critical points: f(x,y) = 3xy-x²-y?

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Q: Suppose that f(x, y) = e¯4z² - ly + 7z + 2y then find the discriminant of f.

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Q: Find and classify all critical points of the function f(x, y) = x³ + 2y4 - In(x³y³)

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Q: Find the best linear approximation to f(x) = ex on the interval [-1,1]

A: We have to find the best linear approximation of f(x)=ex on the interval -1,1.

Q: Let f(x, y) = 4x² + 5xy + 2y? – 2x – 3y +1. Find all critical points, and state what type they are.

A: Given: f(x, y)=4x2+5xy+2y2-2x-3y+1 We have to find all the critical points and state their type.…

Q: Find and classify the critical points of the function f(x,y) = x²y+ 4xy – 2y²

A: The given function is f(x,y) =x2y+4xy-2y2.

Q: Let f(x,y)=x°-4y where 0<x <1 and 0sysl. Find the minimam of value of f(x,y).

A: Answer

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: Find the critical point (x0,y0) of the function f(x,y)=120x+120y−xy−x2−y2

A: A point (a,b) is critical point of function f(x,y) if either ∂f∂x(a,b)=0 and ∂f∂y(a,b)=0 or atleast…

Q: Use the fact that the critical points of f(x,y) are found when Vf(x, y) = 0 to show that (-3,-2) is…

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Q: Let f(r,y) r+ 12ry+12y. Find all the critical values and claesify them.

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Q: Show that the linearization of f(x) = (1 + x)k at x = 0 is L(x) = 1+ kx.

A: We need a linear approximation formula for f(x).

Q: Consider the functions f(x, y) = x2 − y2 and g(x, y) = x2 + y2 .                             (a)…

A: Given functions are f(x,y)=x2-y2  and g(x,y)=x2+y2.

Q: Consider the following function: f(r) = 2r + 3z² – 12z Find the critical numbers of f. (x = ?)

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Q: Let f(x,y) = 5x² + 6y² + 3xy – 5x – 8y + 36 What is the first coordinate of the critical point?

A: Given data:   The given expression of the function is f(x,y)=5x2+6y2+3xy-5x-8y+36.     Equate the…

Q: Given f (x,y) = 3 – 2x² – 2xy – 2y² – 16x, find and classify all critical points of f. -

A: Calculate fx, fy , fxx , fyy , fxy for f(x,y)=3-2x2-2xy-2y2-16x as follows.…