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Consider two variable functionz=x2y+2xy+13y33y.z=x2y+2xy+13y33y. (a) Find the partial derivatives z x and z y . (b) Find all critical points of the function. (c) Determine

Consider two variable functionz=x2y+2xy+13y33y.z=x2y+2xy+13y33y.

(a) Find the partial derivatives z_x and z_y.

(b) Find all critical points of the function.

(c) Determine whether each of the critical points is a saddle point or the function attains a relative maximum/minimum at this point.

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