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The function f(x, y) = x³ − 3 x² y + 3 x y² − y³ + x² + 6 x y − 3y²2 – 1 has a critical point on the x-axis. - (a) (i) Enter fx (x,0) = (ii) Enter fy (,0) = (b) Enter the x-coordinate of the critical point, where both these derivatives are zero. Number (c) Enter the matrix fxx fxy [fyx fyy at that point. To enter the matrix click on the 3 x 3 grid of squares below and replace the entries with your answer. Ə ab sin (a) f ∞ a Ω əx (d) Based on this matrix, what sort of critical point is it? Click for List

There is also a critical point on the y-axis. (e) Enter its y-coordinate. Number (f) Enter the matrix fxx fay fyx fyy ab sin (a) f əx (g) Based on this matrix, what sort of critical point is it? Click for List at that point. 8 a Ω