Let f(x, y) = 5x 2y − 3x2 + 2y3 + 3xy, P be the point (1,...

Let f(x, y) = 5x ²y − 3x² + 2y³ + 3xy, P be the point (1, −2) and a = <3, −5>. This problem has five parts.

(a) [5 pts.] Find the first partial derivatives of f(x, y).

(b) [5 pts.] Find all of the second-order partial derivatives of f(x, y).

(c) [5 pts.] Find an equation of the tangent plane to f(x, y) at P.

(d) [5 pts.] Find ∇f. (This is still part of number 8)

(e)Find the directional derivative of f at P in the direction of a.

Expert Solution

milcah answered 1 year ago

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Question

Let f(x, y) = 5x 2y − 3x2 + 2y3 + 3xy, P be the point (1,...

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Expert Solution

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