Show algebraically that a tangent plane intersects a function more than once

by J. Cricks   Last Updated October 17, 2019 11:20 AM - source

Let $$ g: \mathbb R^2 \rightarrow \mathbb R, g(x,y) = -2x^4 - 4x^2y^2 - 6x^2 -xy^2 - y^2$$

Use algebra to show that the tangent plane at (-1,2) intersects g(x,y) more than once and identify another point of intersection.

The tangent plane is defined as $$48x-16y+56=0$$

How do I algebraically show that the plane intersects the function more than once?



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