Question: Let f : R2 > R be a differentiable function of two variables and let (a, I), f ((11 6)) E R3 be a point

Let f : R2 > R be a differentiable function of two variables and let (a, I), f ((11 6)) E R3 be a point on the graph of f; that is, (a, E), f (a, 6)) lies on the surface in R3 described by the Cartesian equation 2 = f (I, 9)- It is given that the partial derivatives 1;, fig of the function f satisfy (f$(a1 b): fyza b)) 75 (01 U): which means that the tangent plane H, to the graph of f at. (a,b, f (a, b)) is not horizontal. (i) the tangent plane Ht to the graph of f at the point ((1,1), f[a,b)), (ii) the horizontal plane H5 passing through the point (a, b, f (a, b)), (iii) the contour C of f passing through the point ((1,1), f (a, b)), (iv) the horizontal line Lg, that is tangent to C at the point (0,6, f (a, 6)), (v) the vertical plane IL, that contains the line Lb

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