Consider the function F(x, y) = x³ +3x2 - 6xy2² + 2y3, Check whether the function F is concave or convex. C. d. Check whether these critical points can be global or not.

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A: To find critical points of f(x,y) , find fx(x,y)=0 and fy(x,y)=0

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A: Solution is here

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Q: Please show step-by-step solution

A: Given function is Firstly, we will find f'(x) and f''(x)

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A: We will find the critical points.

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Q: Consider the function F(x, y) = x +3x? - 6xy + 2y, Check whether the function Fis concave or convex.…

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A: The given function is  f(x,y)=x2+2y2-4x-4y defined on R2.

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Q: Let f(x, y) = 4x² + 5xy + 2y? – 2x – 3y +1. Find all critical points, and state what type they are.

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A: Topic = Function

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Q: Given f (x,y) = 3 – 2x² – 2xy – 2y² – 16x, find and classify all critical points of f. -

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Q: Find the local extremum of the function • f(x,y) = xy² – 6x² – 3y²

A: Find the local extremum of the function f(x,y) = xy2 - 6x2 - 3y2

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.