Find the absolute maximum of f(x,y) = 7x²y² + 5y² + 9x² bounded by y = x, y = 0 and x = 2.

Q: Identify and sketch the domain of f(x, y) = y² + 4x + 2 In(1-x² - y²)

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Q: Find the maximal value of the function f(x,y)=2x3-y3 on the circle of equation x2+y2=7.

A: We have to find the maximal value of the function  on the circle of equation

Q: Find the maximum value attained by the function x² + xy + y² on the set {(x, y) : x² + y² < 2}.

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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: Which point on the curve y = √x - 4+9 is closest to the point (7, 9)? (x, y) = ( What is this…

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Q: Show that the maximum value of f (x, y) = x 2 y3 on the unit circle is

A: We should maximize f(x,y)=x2y3 under the constraint gx,y=x2+y2 where x2+y2=1. Now, ∇f=2xy3,…

Q: Suppose that x and y are two positive real numbers so that x + y = 10. Maximize the product xy

A: To find the solution of the given problem use the second derivative test. Second derivative test:…

Q: Find the maximum value of f(x,y) = 31-x² - y² on the line x + 5y = 26.

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Q: Let f (x) be the square of the distance from the point (2, 1) to a point (x, 3x + 2) on the line y =…

A: The square of the distance between two points (a, b) and (c, d) = (c - a)2 + (d - b)2

Q: Find the maximum and minimum values of f(x) = x3 − 6x2 + 8 on the horizontal span of 0 to 10.

A: We're tasked with finding the maximum and minimum values of the function f(x)=x3−6x2+8 over the…

Q: Find the absolute minimum and absolute maximum of f(x, y) = (9x² − 1) (1 + 4y) on the rectangle…

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Q: Sketch the domain of f(x, y) = √4x² - y² x - y² on the ry-plane.

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Q: A rectangular plate with an area of 36 cm? is to be produced on a lathe in such a way that the…

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Q: f minimum nction 13x L 6

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Q: Find the maximum value of f(x,y) = 13 – x -y on the line x+ 2y = 5.

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Q: find the maximum value of z = xy2 subject to 2x2 + y2=864;  x ≥ 0, y ≥ 0,

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Q: Determine where y = x4 - 8x2 has a local maximum or a local minimum.

A: we havefx=x4−8x2