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  3. 1.consider the function: f(x, y) = 2020 + y3-3xy +

1.Consider the function: f(x, y) = 2020 + y3-3xy + x3. a) Find fx(x, y), and fye(x,...

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Basic Math

1.Consider the function: f(x, y) = 2020 + y3-3xy +x3.

a) Find fx(x, y), and fye(x, y).

b) Find all critical points of f(x, y).

c) Classify the critical points of f(x, y) (as local max, localmin, saddle).

2.Consider f(x) =2x-x2and g(x) =x2

a) [2 points] Find the intersection points (if any) of thegraphs of f(x) and g(x).

b) [4 points] Graph the functions f(x) andg(x), and shade the region bounded by:f(x),

g(x), x = 0, x = 2.

c) [8 points] Find the area of the shaded region.

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