6. Find the absolute maximum and minimum of the function f (x, y, 2) = x + 2y on the intersection curve between the plane x + y + % = 1 and the cylinder y? + z² = 4.

Q: Find the minimum of f(x,y) = 2x2+3y2 subject to x2+y2=4.

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Q: S (x, y)= I+x* + y? 1-x² - y? 2. Determine the points at which the function is continuous.

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Q: Find the points on the circle x? + y? = 1 in which f(x, y) = 4xy has an absolute maximum and the…

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Q: Exercise 4. Show that the function f is not differentiable at (0,0) f(x, y) = x³ + y³

A: We have given that ,  fx , y = x3 + y33 Here , ∂f∂x = 3x23x3 + y323 ∂f∂x = x2x3 + y323 At , x , y =…

Q: ye-(²²+y²+z²). Find all points (x, y, z) such that Vf(x, Y, z) = Question 2. Consider the function…

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Q: What is the maximum of the function f(x, y) = 2xy + 2x - 2x2- y? а. (х, у) %3D (1, 1) Оь. (х, у) %3D…

A: find the partial derivative and set to zero to find the maximum and minimum value

Q: Suppose that f(x, y) = 2x² + 2y² - 2xy Then the minimum is

A: Given the function is:f(x,y)=2x4+2y4-2xy

Q: Find the maximum and minimum of f(x,y) = yx2 + y(y - 1)2 subject to x2 + y2 =1.

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Q: et f(z, y) = for (z, y) # (0,0). Find the level curves of 2 + y²

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Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: 13 Find the linearizatian z=L(x.y) f the function 2=f(x.y) =4x²-y²42y at the point (x.y) = (3,2).…

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Q: Integrate the function f(r,y, z) = Over the entire 3D coordinate system, i.e., all of R'.

A: We have to integrate the function fx, y, z=1x2+y2+z21+x2+y2+z2 over the entire 3D coordinate system,…

Q: . Use the second-derivative test for local extrema (: extrema for the function. Identify whether the…

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Q: Suppose that f(x, y) = 2x² + 2y¹ − 2xy Then the minimum is

A: Given function: f(x,y)= 2x4+2y4-2xy partially differentiating f w.r.t. x, ∂f∂x= 8x3-2y partially…

Q: Q2: Find the absolute maximum and minimum of the function f(x, y) = x² + y² on the closed triangular…

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Q: 4. Let f(x, y) = y³ +32²-6ry-9y-2, Find absolute maximum and minimum of this function on the…

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Q: The temperature T in a square region of the (x, y) plane is given by the formula T(x, y) = 2 y – x +…

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Q: Let f(x, y) = √x² + y² - 4 y 2 - Identify the equations of the level curves of f for k = 0, 1.…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…