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4. Consider the function z = f(x, y) = x^(2) + 4y^(2) (a) Describe the contour...

4. Consider the function z = f(x, y) = x^(2) + 4y^(2)

(a) Describe the contour corresponding to z = 1.

(b) Write down the equation of the curve obtained as the intersection of the graph of z and the plane x = 1.

(c) Write down the equation of the curve obtained as the intersection of the graph of z and the plane y = 1.

(d) Write down the point of intersection of the curves in (b) and (c). Call this point P = (x0, y0, z0)

(e) Calculate ∂z/∂x, and give its value at point P.

(f) Calculate ∂z/∂y , and give its value at point P.

(g) Calculate the change in z when (x, y) changes from to (x0, y0) to (x0 + 0.1, y0 + 0.1).

(h) Approximate the change in z by fx(x0, y0) × 0.1 + fy(x0, y0) × 0.1

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