Find, if they exist, the extrema of the function: f(x, y) = x² + 3y? + 4,

Q: Find the extrema of f(x,y) = xy + 14 subject to  x2 + y2 = 18.

A: To Determine: Find the extrema of f(x,y) = xy + 14 subject to                         x2 + y2 = 18.…

Q: What does it mean for a function of two variables, f (x, y),to be differentiable at a point (a, b)?

A: A function differentiable at a point has a derivative that is defined at that point. This is defined…

Q: Find the extrema for the function: = f(x,y) = x²y2 - x² – 3y3 %3D

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Q: Find and sketch the domain of f(x, y) = √√1 − (x + 1)² − y² + 2 ln (x − y + 1).

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Q: For what vaļue of x does the function g(x) =x - 2x? strictly convex? В. x> 0 A. x> 2 D. x -2

A: From the given problem:   gx=13x3-2x2   As we know that:   If f''(x)<0. then function strictly…

Q: Fundamental Theorem of Calculus.

A: ∫abfx dx

Q: Consider the function f (x, y, z) = x² + y – xyz Find grad

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Q: Consider the function f(x) = a²e15z. f(x) has two inflection points at x = C and x = D with C < D…

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Q: Examine the function f(x, y) =-3x-4y+15x - 16y + 6 for relative extrema.

A: Here we have to find relative maximum.  The solution is in both 1st and second steps.

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 10 T, and the line perpendicular…

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Q: f(x, y) = x² – y²

A: f(x,y) = x2 - y2 Let us firstly find the first order partial derivatives of the given function.…

Q: Consider the function z = ƒ(x, y) = 9x3 - 8x2y + 4y3.;Find dz.

A: Consider the given function, z=fx,y=9x3-8x2y+4y3 The formula of the total derivative dz is,…

Q: The level curves of the function f (x, y) = Vx² – y² – 1 are

A: We have to find the level curves .

Q: Find the linear approximation of the function below at the indicated point. f(x, y) = V 17 – x2 –…

A: Givenf(x,y)=17-x2-4y2  Point (2,1)

Q: Find and sketch the domain of the function In(x + y) f(x, y) 1– y?

A: From the given information. The function in x and y is as follows. fx,y=lnx+y1-y2

Q: Show that the function f(x, y) = (y + ax)?e+ax satisfies the equation given by ах dy?

A: It is partial derivative problem

Q: Find the direction in which the function is increasing most rapidly at the point P 0. f(x, y) = xy 2…

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Q: Find a2z given that z is a differentiable function of x and y, and xz + yz3 = 2 + x²e♥

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Q: Find f(x), the most general antiderivative of the function: f' (x) = 3x –

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Q: Find f, (x,y) and fy (x.y), and explain why f(x,y) has no local extrema. f(x.y) = 8x + 3y + 4. fy…

A: It is partial derivative

Q: Find the linearization of the function f(x, y) = V61 – 3x2 - 1y? at the point (4, 2). %3D L(x, y) =

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Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y* + + 4y – x16

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Q: Find R of the function Y = f(x) = vx %3D

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Q: Exercise 1 Determine the relative extrema of f. (a) f(x, y) = 18x² – 32y² – 36x – 128y – 110

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Consider the function f(x,y) = x² + xy – 5x – y+ 1. Then:

A: Consider the given function as fx,y=x2+xy-5x-y+1

Q: Find the absolute maxima and minima of the function f (x,y)=2x²-4x+y²-4y+1 on the closed triangular…

A: Given:The given function is f(x,y)=2x2-4x+y2-4y+1 on closed triangular region bounded…

Q: 11.2.4. f(x, y) = V]xy|.

A:

Q: Find all local extrema for the function f(x.y)= 4y-128y +3x -11.

A: Given,  f(x,y)=4y4-128y2+3x2-11

Q: Find all the relative extrema of the given function below: f(x, y) = 3y² – 2y³ – 3x² + 6xy.

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Q: Calculate the approximation of My for the given function and interval f Cx)=フメーンLュ,3 %3D

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Q: For the function f(x,y,z) = 1 + xy“ - 2z*, find fy, fy, and f,. fx f2

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Q: Find f, for the function f (x, y) = yx-2z'y %3D

A: we have to partially derivative

Q: For which values of a ER is the function f(r + iy) = (a²x – axy) + i ax? + ay %3D an entire…

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Q: Consider the function f(x, y) = x² + xy - 5x- y+1. Then:

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Q: Consider the function f(x, y) = Va+y+I x-1

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Q: Find all local extrema for the function f(x,y) = - 6x - 9xy - 4y + 72x+54y+ 6.

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Q: Find the domain of f(x, y) = Vy+I y(1-x²)

A: Given: f(x,y)=y+1y1−x2 The domain of functions of two variables, f(x,y) are regions from two…

Q: Find the absolute maxima and minima of the function f(x, y) = x² + y² on the closed triangular plate…

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Q: · y = Vx - x, (1, 0)

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Q: Find the absolute maxima and minima of the function f(x,y)= 2x^2-4x+y^2-4y+1 on the closed…

A: See the explanation below

Q: The antiderivative of the function f(2) +7z is

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Q: Show that the function d: RxR → R defined by d(x, y) = √x-y

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Q: Consider the function z = f(x,y). If fx(a,b) and fy (a, b) both exist, and they are equal, then the…

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Q: The domain of the function f(x, y) = 3x + xy + 5y? is R.

A: We have to verify that the domain of the function fx,y=3x+xy+5y2 is R or not.

Q: Is g(x) = Vx + 1 differentiable or not? Justify.

A: Note :-  f(x) is exist only if f(x)≥0.

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: If z = y + f(x^2-y^2), where f is differentiable, show that y(∂z/∂x) + x (∂z/∂y) = x.

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Q: Consider the function f(x, y) = 4x² – 8y² subject to the condition x + y = 25.

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Q: find the extrema for f(x,y)= x^3 +y^3 -6xy

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.