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Tangent Plane

發問:

Find a point on the surface z=3x^2-y^2 at which the tangent plane is parallel to the plane 6x+4y-z=5

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Let f(x, y, z) = 3x2 - y2 - z Then, grad f = 6x i - 2y j - k (bold letters represent vectorial quantities) For parallel to the plane 6x + 4y - z = 5, we have x = 1, y = -2 Hence z = - 1 Threfore the point is (1, -2, -1)

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