(a) If the graph of a function f .x; y/ that is differentiab

Question and Solution

(a) If the graph of a function f .x; y/ that is differentiable at .a; b/ contains part of a straight line through .a; b/

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(a) If the graph of a function f .x; y/ that is differentiable at .a; b/ contains part of a straight line through .a; b/, show that the line lies in the tangent plane to z D f .x; y/ at .a; b/. (b) If g.t / is a differentiable function of t, describe the surface z D yg.x=y/ and show that all its tangent planes pass through the origin.

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