Find all critical points of the function

Reference no: EM13938018

(a) Find all critical points of the function f(x, y) = x 3 + 3y - y 3 - 3x and classify them as local minima, local maxima or saddle points.

(b) For each critical point (x0, y0) you have identified in part (a) above, calculate the Taylor series expansion of f(x0 + δx, y0 + δy) about the point (x0, y0) up to (and including) quadratic terms. By considering in each case the sign of f(x0 + δx, y0 + δy) - f(x0, y0) for all δx and δy of sufficient small magnitude justify your conclusions in part (a)

Reference no: EM13938018

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