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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.3 Tangent Planes and Linear Approximations, #16 · Multivariable Calculus · Partial derivatives

If the normal line at every point on … goes through …

If the normal line at every point on $F (x, y, z) = 0$ goes through $(0, 0, 0)$ , show that $F_{x} = c x, F_{y} = cy, F_{z} = cz$ . The surface must be a sphere.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.3 Tangent Planes and Linear Approximations, #16

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