3. Consider the function f and region D as follows: 3 f(x,y) = x³-x-y² D= (x, y) + y² x2 4 ≤1} (a) (8 points) Find all critical points of f in the interior of D (not including the boundary), and classify them as either a local minimum, local maximum, or saddle point. (b) (12 points) Find the absolute minimum and maximum values of f in D (including the boundary).

Q: 3) Given that f(x) =x2+8 / x2−4 a. Find the stationary value(s) and indicate whether they are…

A: The given function is - f(x) = x2+8x2-4

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A: Here is the solution of the given problem. Maximum and Minimum over a Region.

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A:

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A: By using Second Derivative Test find Critical Points and Absolute Extreme Values.

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A:

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A:

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Q: • Let S be the graph of f(z, y) = r² + y² – 2r + y for (1, y) E D = {(1,y) : r +y < 4 and z+ y 2 0}.…

A: Consider the given information.

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A: To Determine :-  The absolute maximum and minimum values of f on the set D , where  f  x , y  = xy3…

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A: We have to find 1st and 2nd partial derivatives.

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A: According to the given data, find the Absolute minimum and maximum of f(x,y):

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Q: The absolute minimum values of f(x) = x³ – 3x +1 -3sxs3 is a) 19 b) 2 c) - 1 d) – 17

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Q: a. Let f: R" →→ R, and a € R". Prove that the following two statements are equivalent: • Du[f] (a) =…

A: note :Since you have posted multiple questions, we will provide the solution only to the first…