what sets X and Y is the function X Y defined by 3x f (x) = x +4 %3D ijection?

Q: The local linear approximation for f (x) = Vx2 + 16 near x = -3 is

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Q: Find the maximum and minimum value of f(x,y) =x3+3xy2-3x2-3y2+4

A: fx,y=x3+3xy2-3x2-3y2+4   fx=3x2+3y2-6x   fxx=6x-6   fxy=6y   fy=6xy-6y   fyy=6x-6

Q: 2. Find and classify the critical points of the function f (x, y) = 6x2 – 2x³ + 3y? + 6xy

A: The solution is given below in the next step:

Q: Find all points (x.y) where f(x.y) may have a maximum or minimum. f(x,y) = - 3x + 5xy- 2y² +x+y

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Q: The critical points of the function f(x, y) = x³ + xy + y² are _____.

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Q: Find the function y(x) satisfying dx2 = 12 - 12x, y'(0) = 5, and y(0) = 8. ay = 12- 12x, y'(0) = 5,…

A: an initial value problem  is an ordinary differential equation together with an initial condition…

Q: Examine the function f(x, y) = −3x² - 4y² + 15x - 8y + 5 for relative extrema.

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Q: 21) Find the maximum and/or minimum values of f (x, y) = x² + 2xy + 2y² - 6y + 2

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Q: 3. Find the relative extrema using any method. f(x) = (3xe*)².

A: A function f(x) has relative extremum at a point x=a if f'(a)=0. We first find the derivative of f…

Q: Find f, fy. f- f(x.y.z) = 3x - 4y 2. 2 +z?

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Q: : Express the function f (x) = e") to the form u(x,y) + iv(x,y).

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Q: Examine f(x,y) = 2x2 - 4x +xy2 - 1 for relative extrema?

A: Calculate fx, fy , fxx , fyy , fxy for f(x,y) = 2x2 - 4x +xy2 - 1 as follows. f(x,y) = 2x2-4x+xy2-…

Q: A function f : R? → R is given by f(x,y) = y² + 2x² – x²y. Find and classify its critical points.

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Q: Find and classify the critical points of the function f (x, y) = 16x³ – 12x2 + 12xy? + 3y?

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Q: Find the domain and range of the function f(x, y) = exy

A: Given information: The function fx,y=exy

Q: 1. Let f(x, y) = 8x³ + y³. Find fæ(0,0). %3D

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Q: Find the area of a triangle bounded by the y axis, the line f(x)=4−(6/7x) and the line…

A: Formula Used: Area of triangle is :                                   Where,  b is base of triangle…

Q: Find the general antiderivative of the function. (If nec- essary, rewrite the function before…

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Q: 2. For what value of k will x – iky F(x, y) = (x+ y)² + be analytic?

A: Given function is fx,y=x+y2+x-ikyx+iy If it is analytic then it satisfy C-R equation ux=vyuy=-vx

Q: Find the absolute maximum and minimum values of f(x, y)=x² +xy+y² -6y on D={(x, y)| -3<x<3, 0<y<5}.

A: Given curve is f(x,y) = x^2+y^2+xy-6y  Find critical points

Q: f(x, y) = 4x² – y²

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Q: Determine the global extreme values of the function f(x, y) = 2x³ – 4y, 0< x, y < 1 fmin fmax

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Q: Maximize f(x, y) = 3xy Зху subject to x + y = 1

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Q: Maximize f(x, y) = 18 - x2 - y2, x + y - 2 = 0.

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Q: Find the maximum and minimum values of f(x, y)=x+3xy2-3x2-3y²+4.

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Q: Find the values of x, y and z that correspond to the critical point of the function: 23D f(+, у) —…

A: Given  z = f(x, y) = 2x2-6x-3y+3y2+5xy We have to find the critical point of the function.

Q: Find the maximum value of f(x,y) = 25 - x - y on the line x+ 4y = 17. %3D

A: First-order derivative test for Maximum value : - The slope of a function is determined by its first…

Q: f (x, y) = -2x – 4.xy + 2y? + 2x – 2

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Q: Identify the removable discontinuity. x² – 1 f(x) : X- 1 (х, у) %3D Additional Materials

A: A removable discontinuity is one at which the limit of the function exists but does not equal the…

Q: Find the relative maximum and minimum values. f(xy) = 4x - 2y?

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Q: Find fg, fyand f; if f(x,y,z) = x - Vy² + z²

A: Given:     To determine: Partial  derivative  fx, fy, fz

Q: Find the maximum and minimum values of f(x, y) = (x- y) e- + y)

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Q: Find the maximum and minimum values of the function f(x, y) = e²Y subject to + y° = 16

A: Given data: The expression for the first function is f(x, y)=exy. The expression for the second…

Q: What value of b >-1 maximizes f(b) = J - x) dx!

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Q: Find the maximum and minimum values of the function f(x, y)-xy subject to g(x, y) = x² + xy + y² =…

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Q: Consider the function f(x, y) = e-xy It is possible to state that f reaches global extremes (global…

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Q: |Classify all critical points of f(x, y) = x²y² – y? + 2x² – 12x.

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Q: Find the particular sölution f"(x) = 4, f'(2) = 12, f(2) = 17

A: integration 2 times and after applying initial condition we get f(x)

Q: A consumer has utility function xy u(x, y) = x+y

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Q: Find the maximum value of f(x,y) = 13 – x -y on the line x+ 2y = 5.

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Q: Give an example of a linear function f(x)= mx + b, with m,b ±0 and an interval a<xsc where f(x)dx=0…

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Q: maximize f(x,y)=xy subject to the contraint 6x+y=18  the last question is what is the maximum valye…

A: max . fx,y=xyS.t 6x+y = 18     6x+y=18⇒ 6x+y-18=0∴ gx,y=6x+y-18=0    Fx,y,L=fx,y-L g x,y⇒…

Q: Find the critical point of the function f(x,y) = 7x²y² + 4y² + 4x².

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Q: Find the absolute maximum and minimum of f(x, y) = 1x + 5y within the domain 2² + y? < 1². %3D

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Q: Determine the extrema of the implicit functions: (2² + y² + z²)² = 1 – a² – 2², z = 2(x, y) | |

A: Given x2+y2+z22=1-x2-z2 Differentiate with respect to x:…

Q: 2R then the constants R TCX If f(x) Rsin .2 S,f' and f(x)dx and S are respectively.

A: Introduction :Here we have asked to find the value of R and S

Q: Find the largest domain (in R²) for the function 1+ Vx + Vy x² + y? f(x, y) =

A: The domain are those values of x,y; such that f(x,y) is well defined. Well defined means that the…

Q: Describe the domain of : f (x,y) = Ln(2 + x + y)

A: in the question it is asked to write the domain of f(x, y)=ln(2+x+y).