S(x) =- x-2 y 8(x)= Vx

Q: Find all values of x such that dy/ldx = 0 where y is the function stated below. x2 y = -3x + 4)

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Q: Find the linearization of the function f (x) = x' at x = 1. L (x) =

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Q: The critical point of the function* f(x, y) = x² + 5y² + 2 cos x

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Q: z = x3 – xy? + 3y2

A: Let us consider the two variable function z=f(x,y) The first partial derivative of the function is…

Q: Find the maximum and minimum values of the function f(x, y) g(x, y) = x² + xy + y² = 27 ry subject…

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: (b) Integrate f(x, y) = 4e0.8x - 0.5y using h = 0.5 with y(0) 2 from x = 0 to 0.5.

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Q: (b) Find the first order partial af and ду af Əx ay for the derivative f(x y) = 2x² sin(x+ )…

A: To find the df/dx of partial first order differential we differentiate function with respect to x…

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

A: The solution of the problem is given in the next step.

Q: Find the linearization L(x) of the function f(x)=x^3/4 at x=1

A: Given, f(x)= x³/4 x=1 Therefore, f(x=1)=1³/4 f(x=1)=1/4

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: Find the partial derivative fx for the function f(x,y)=√16x+y³ |f₂(x, y) = O f.(x,y)= f₂(x, y) = 1…

A: We have to find derivative

Q: Find the partial derivative. z = (2² + 2x – 6y)"

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Q: Find all stationary (critical) points of the function g(x, y) = x³ + y³ + 3x² + 3y + 3x + 3xy +1.

A: First calculate the partial derivatives, gx, gy  for g(x,y) . Solve the equations, gx=0 , gy=0…

Q: Differentiate the function. y=In(x²+e' y=In(x²+ean x)

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Q: What is the mixed, second order partial derivative of this function. f (x, y) = / 2x² + y²

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Q: Suppose that f(x, y, z) = (1+x + y² + z³)4 + ln (1 + 3x + 2y + z).

A: In this question, we approximate the function by using a linear approximation of f(x,y,z)

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

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

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Q: (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: Let us find the four second partial derivatives of the given function in the next steps.

Q: Find the partial derivative Əz Əx for the function z = 8y²√x.

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

A: Given, f(x)=x6

Q: Find the critical point of the function f(x, y) = x² + y² + xy +7.5x C=

A: To find the critical point of the function fx, y=x2+y2+xy+7.5x.

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a =. 3 L(x) =

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Q: Find the critical point/s of the function f(x,y) x³+2xy-2x-4y

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Q: Supposed that z is defined implicitly as a function of x and y by the equation x2 + y2 +z2 = 4. Find…

A: The given data is: x2+y2+z2=4 To find the value of dzdx

Q: Find a multivariable function f(x, t) that satisfies the Black-Scholes equation: ft = f - xfx -…

A: f(x,t)=etlog(x) satisfies Black-Scholes equation: ft = f - xfx - x2fxx

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: f(x, y) = 3xy – x²y- xy?

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Q: find ∇f at the given point. ƒ(x, y, z) = x2 + y2 - 2z2 + z ln x, (1, 1, 1)

A: Given function is fx,y,z=x2+y2-2z2+zlnx and point=1,1,1

Q: Find the linear approximation L(x)of f(x)=x^4 at the point a = −5 L(x)=

A: Given that f(x) = x4 We have to find the linear approximation L(x) of f(x)=x4 at the point a= -5.

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = 3 L(x)

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Q: Find the differential dy of each function: a) f(x) = 2x^1/3 - 3x^1/2 b) f(x) = ( x^2 +1) / (x+1)

A: we will find the derivative of given function using basic differentiation rules.

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: x2 ) Find f(1) if / f(t) dt = x° – x* + 2x² – 2 , x>1.

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Q: Differentiate the function. y = In(e-X + xe¬X) y' = II

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Q: Find the first partial derivatives of the function. x5 - y5 x° + y f(x, у)

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Q: Find the linearization L(x) of the function at a. п f(x) = sin(x), a = 6 L(x) =

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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: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

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

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Q: Find the critical point (x0,y0) of the function f(x,y)=(√(x2+y2))+1.

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Q: Find and classify all critical points of the function defined by h(x,y)=x^3−3x+3xy^2.

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Q: Find the partial derivative of fy for the function * 3 f (x, y) = (3x² + y²) ³ 3x² (3x² + y²)²…

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Q: Find the linearization of the function f(x)=x2+2cosx at a=0.

A: Linearization of a function f(x) at x = a is given by, Now,

Q: Find the partial derivative 9. f(x, y) = x ^ 4 + 5x * y ^ 30

A: Given,            f(x,y)=x4+5xy30

Q: Find constants c1 and c2 such that F(x) = c1xe -x + c2e -x is an antiderivative of f(x) = 3xe -x .

A: Given: Fx=C1xe-x+C2e-x  and fx=3xe-x

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) 4x? – 4x…

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Q: Find f(3,4) for f (x, y) = ln(x + Vx² + y²).

A: We have to find out the derivative