Suppose that f is a differentiable function of one variable. show that all the tangent planes to the the surface z = xf (y / x) intersect in a common point.

If is a point on the surface, then the cartesian equation of the  tangent plane at is

,

where .

Given that

, then

becomes

.

Finally, replacing in you have that the equality is true for all . This means that

belongs to all tangent planes and therefore, the result follows.      

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step-by-step explanation:

distance formula is d=√(x2-x1)^2   +   (y2-y1)^2