8. (a) T F The xy-trace (on the xy-plane) of the surface x² + y² − z² = 0 is a point. (b) T F If f(0,0) exits and g(x) = f(x,0), then ƒ(0, 0) = g′(0). (c) T F If f(0, 0) = 0 and fy(0,0) = 0, then f(x, y) has a local extreme at (0,0). (d) T F If f(0, 0) and fy(0,0) both exists, then f(x, y) is differentiable at (0,0). (e) T F If f(x, y) is continuous on the disk D = {(x, y) | x² + y² ≤ 1 }, then ƒ(x, y) has an absolute maximum on D.

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