Find the extrema points of f(x,y) =x3+6x2+3y2-

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: 3. Find fz and fy where f(x,y) = In(x + y²).

A:

Q: 2x :S dr f(x, y) dy. f (x, y) dy. •1-x² f (x, y) dy. -V1-r

A:

Q: Find fzyæ. f(r, y, 2) = a'y"2³ + xy® + y°z %3D f zyz

A: Given f(x,y,z)=x^4y^7z^5+xy^6+y^7z

Q: Integrate f(x, y) = 4c®* - 0.5y using h = 0.5 with y(0) = 2 from x =0 to 0.5.

A:

Q: f(x, y) = /2x – y /2х — у f(x, y) = In(9 – x² – 9y²) f(x, y) = /1 – x²? - VI – y² S(x, y) = Vy + /25…

A:

Q: Vx? + yZ 49x2 49 [F,(x, y)]² + [f,(x, y)]² 1+ x² + y2 e have [f,(x, y)]² + [f,(x, y)]² = /

A: This is the question from vector calculus.

Q: Find fzyæ. f (x, y, z) = x°y®°z° + xy° + y°z f zyr ||

A:

Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

A:

Q: f(x, y, z) = xyz + xy3 + yz3 + zx3 %3D fy

A:

Q: Find the local extrema and saddle point(s) of f (x,y)=x*y-6y² – 3x² .

A:

Q: Maximize and minimize the function f (x, y) = 1+ 4x + 2y – 2x2 – y? on the triangle bounded by the…

A: We will find out the required value.

Q: Find fz(x,y) and fy(x, y) given f(r, y) = csc yArcsin(r²).

A:

Q: 2) f(x, y) = x +y on the closed triangular plate bounded by the lines x 0, y= 0, y+2x = 2 in the…

A:

Q: Find fzyz. f(r, y, z) = x*y³zª + xy" + y°z f zyz

A: Given-  fx,y,z=x4y3z4+xy7+y6z To Find- fzyx

Q: Find fzyx. 8.8 f(x, y, z) = x*y°z® +xy³ + y°z f zyz ||

A: GIVEN: f(x, y, z) = x4 y8 z8 + xy5 + y5 z

Q: Q4/ Linearize the Function Z = XY2 About X, = 3, Y, = 6 using: a) Absolute Variables b) Perturbation…

A:

Q: b) Given z = f(x -y, 2x - 2y, 3x – 3y). Show that dz dz 0. ду

A: The solution is given as

Q: 2. (a) Find the linear approximation L(x, y) near the point (1, 2) of the function f (X,Y)=(0=Y) +…

A:

Q: Find the ditterential of the function y = (x + 1(5x - 3). Sx-x-5 dy = (Sx - 3) *?+ 6x-5 (5x- 3)? dy…

A: Use the quotient rule of differentiation ddxuv=vdudx-udvdxv2. Power rule of differentiation…

Q: Find the extrema of the function f (x, y) =x² + y² + x²y + 4 in the domain D={(X, Y), 1X1 <1, iyi <…

A: See the attachment

Q: dz dz and of the function xsin(y+ z) – xy + z² = 2y. ду -. Find the əx

A:

Q: Find fy(x,y) and fy(x,y). Then, find fy(- 1,4) and fy(1, – 4). 5x3y f(x,y) = e Xy +3

A:

Q: max f(x, y, z)=x+2z s.t. x+y+z=1 is (x. y. 2) = (0. - 12/2) with Lagrange multipliers equal to ₁ = 1…

A: In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the…

Q: Find fæ, fy, and fz. 4.5 f (x, Y, z) = 4z In(x*y° cos(5z))

A: To find the partial derivatives with respect to x ,y ,z.

Q: Integrate f(x, y) = y(x² + y³) 3 over the domain x² + y° 0.

A: Given function is fx,y=yx2+y23 and domain is x2+y2≤4 with y≥0 We have to integrate fx,y=yx2+y23 over…

Q: Find fr and fy- f(x, y) = 7e dt f-(x, y) = f,(x, y) =

A:

Q: Find V x F for F(x, y, z)= - -xZ + y² i+ -yz x² + y² =j+√x² + y²k.

A:

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 fy(x,y) and fy(x,y). Then, find fy(- 3,1) and fy(1, – 4). f(x,y) = In |7 + 4x°y²|

A: Let f(x,y) be the given function .Then fx is the derivative of f with respect to x  , treating y as…

Q: (a) Find the critical point of f(r, y) = (4x² – 3) (2² + 43y). (x, y) (b) Find the discriminant,…

A:

Q: f (x, y) = xª – 2.x² + y² – 4y + 5. a) Use the second derivative test to find the critical points b)…

A:

Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation to approximate the…

A: Given: hx=x4 To approximate the values of 34 and 44 using linear approximation of hx. Note: the…

Q: Find fzyz. f (x, y, z) = x°y°z° + xy° + y°z %3D 6-

A:

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

A:

Q: 2L, - 2L <I< 0 f(z) = f(x) %3D 2L- r, 0SI< 2L

A: Given, To find the Fourier series of on is where, and

Q: x² + y² = (2x² + 2y² – x)', (0,¿), (cardioid) -

A:

Q: 1. Find the extrema of the function f(r, y) = y(x² + (ln y)²), y > 0.

A: fx,y =y x2+lny2 ,y&gt;0 first we need to find critical point of given function  so first find first…

Q: [2xy + yz (i) F(x,y, z) = x2 + xz with domain R³. || xY

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1. f(x, y) = 1- x - y 2. f(x, y) = xy 3. f(x, y) = Vx² + y² 2

A:

Q: 1. f (x, y, z) = x° ỹ + 4z°y² – xyz + x² – Vz -

A: Given that: f(x, y, z)=x3y+4z3y2-xyz+x2-z53               NOTE: As per our answering guidelines, we…

Q: 2xy F(x, Y) =Vx+ 2y (1, 1) f,(x, y) = 1,(1, 1) S(1, 1)

A:

Q: ². I = fő fő fő (x + y + z) dx dy dz

A:

Q: -f(x,y, z) = 2z3 – 3(x² + y²)z + tan-1 xz , (1,1,1)

A:

Q: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

A:

Q: © f(X,y) = x4 + 'onY -10 © w = x*y - 10yZ z³ + 43X – 7tan (4Y)

A: It is partial derivative

Q: ntegrais. I, da, D= {(x.y) 0sxs20sys2% dA, D = x +2 [['e"d4, D={(x,y)| 0s ys 4,0sx<y}

A: Double integration

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.