Let g(x,y) = xy-x3-y2. Find the critical points of g and use the second derivatives test to classify the critical points of g

Q: Find the derivative using the theorems on derivatives. dx x2-2 1 y = 2.y = (x² – 1)³(x² + 3)² x3+4x…

A: Given functions to be differentiate are    1.   y=x2-2x3+4x    3.  y=x2-2x      we will make use…

Q: The derivative of the function y = (10e* – 10x*)(tan x) is: a. y' = (e* – 40x3) tan x + (10e* –…

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Q: Find the Partial Derivatives of the functions with respect to each variable X+y 6) f(x,y) = -у' -1…

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Q: Find the second partial derivative for the function z = x7-7xy + 6y2 with respect to x.

A: Solution of given question is written in below steps.

Q: Find the first partial derivatives with respect to x, y, and z and evaluate each at the given point.…

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Q: Given f(x, y) = x²y – 2xy + x² – 2x + y² – y. (a) Find the critical points of f. (b) Use the Second…

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Q: Determine the critical points of f(x, y) = 4.xy-a -y". Then, using the Second Derivative Test,…

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Q: Use the second derivative test to identify any critical point and determine what each critical point…

A: Critical point: The point where the function fx, y is defined and its gradient is a zero vector or…

Q: For the function f(x, y) = Vx³ + y³ find both partial derivatives at the point (0,0) (separate by…

A: Given function, f(x,y)=x3+y33

Q: Given the function f(x) = (x-2)2 + (y-3)2 (i) Find the critical points. (ii) Using the second…

A: The given function is: f(x,y)=(x-2)2+(y-3)2

Q: Calculate all four second-order partial derivatives of the function f(x, y) = x² + 2xy + y² You must…

A: take the partial derivative with respect to x

Q: f (x, y) = 3xy(x + 2y – 6) -

A: By second derivative test ,

Q: If f(x,y) = 8-2x3-6xy-3y2, locate the critical points of f and use 2nd derivatives test to find the…

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Q: 3) To find the partial derivative of f (x. y) with respect to y at the point (xy. we A)…

A: Solving the question with an example

Q: Find the first partial derivatives and evaluate at the given point. Function Point f(x, y) = Invxy…

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Q: Find the first and second order partial derivatives for z x2 sin (3x + 2y).

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Q: of ) Find the first order partial derivative of and for the function f (x, y) = x/y -x²y+y² ây

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Q: Let ƒ (x, y) = x³ − x² − 8x + 2xy − - - 12y². (a) Compute all first order and second order partial…

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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: Find the Partial Derivatives of the functions with respect to each variable 8) f(x, y) = In(x +y)

A: When take partial derivative with respect to one variable consider other variable as constant.

Q: f(x, y) = ex + tan(x + y2).

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Q: Find all the second-order partial derivatives of the functions 41.ƒ(x, y) = x2y3 - x4 + y5 42. z = x…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 4. Find and classify the critical points of the given function by using Second Derivatives Test. 1 1…

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Q: Find the partial derivative of f/x and f/y f(x,y)=x/x+y

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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: f (x, y) = 3x^3 −9x+9xy^2. Use the second derivative test to classify the critical point (1,0) as a…

A: Recall: second derivative test : (i)  Firstly find critical points . i.e, fx(x,y) =0 and…

Q: Find all second order partial derivatives of f(x, y) = 6x²e3y

A: Consider the function fx,y=6x2e3y

Q: Find the first and second order partial derivatives for z = x² sin (3x + 2y).

A: As we know that; The product rule: f·g'=f'·g+f·g' The chain rule: fgx'=f'gx·g'x And The first order…

Q: Find the first partial derivatives of the function. f(x, y, z) = x7yz2+ 4yz

A: From the given problem:   fx,y,z=x7yz2+4yz   So,   fxx,y,z=∂f∂x=∂ ∂ xx7yz2+4yz=∂ ∂ xx7yz2+∂ ∂…

Q: Find all the second-order partial derivatives of the functions g(x, y) = cos x2 - sin 3y

A: Find all the second-order partial derivatives of the functions g(x, y) = cos x2 - sin 3y

Q: Find the first partial derivatives of the funct f(x, y) = x8 + 7xy5 fx(x, y) =

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Q: If the derivative of an analytic function f is 0, does that mean that the partial derivative of f…

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Q: 2) Let f(x, y) = x sin(2y) + 5y¹. Find fyyyyyyyyyy (x, y) (10 partial derivatives), explaining how…

A: Here the given function is f(x,y)=xsin(2y)+5y4x. We have to find the 10 times partial derivative of…

Q: Find all the first and second order partial derivatives of f(x, y) = -4 sin(2x + y) + 1 cos(x – y).

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Q: (b) Find all first and second partial derivatives of z = x² In(x² + xy).

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find all the first and second order partial derivatives of f (x,y) = 10 sin (2x+y) + 3 cos (x−y)…

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Q: Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the…

A: Given

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

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Q: Find partial derivative of: z=f(x,y)= e^x^2+y^2  +   cos(x+y^2

A: For this question of partial derivative we need to find out first derivative with respect to x and y…

Q: How are the partial derivatives ∂ƒ/∂x and ∂ƒ/∂y of a function ƒ(x, y) defined? How are they…

A: Consider the provided information, How are the partial derivatives ∂f∂x and ∂f∂y of a function fx,y.…

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 mixed partial derivative at the point (2, 3) for h(x.y) = x sin(y) + y sin(x) + xy

A: The given function is, Differentiate the above expression with respect x partially.

Q: Find the Partial derivative of f with respect to y for * f (x, y) = x+y

A: →While calculating ∂f(x,y)∂y , consider 'x' as constant.→∂∂yuv = v∂u∂y-u∂v∂yv2

Q: Let f (x, y) = x3 – 3xy + y3. Find all critical points of f and at each critical point, - use the…

A: Critical points using second derivative test

Q: Find all the second-order partial derivatives of the functions w = x sin (x2y)

A: Given function is w=xsinx2y. To find all the second-order partial derivatives of the function.…

Q: Let f(x,y) = 3x4 - 4x³y + 2x2y2-y. Let f, be the partial derivative of f(x, y) with respect to x.…

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