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Suppose you need to know an equation of the tangent plane to a surface S at the point P(3, 1, 4). You don't have an equation for S but you know that the curves r1(t)= <3-3t, 1-t^2, -4t+t^2> and r2(u)= <2+u^2, 2u^3-1, 2u+2> both lie on S. Find an equation of the tangent plane at P.

Suppose you need to know an equation of the tangent plane to a surface S at the point P(3, 1, 4). You don't have an equation for S but you know that the curves r1(t)= <3-3t, 1-t^2, -4t+t^2> and r2(u)= <2+u^2, 2u^3-1, 2u+2> both lie on S. Find an equation of the tangent plane at P.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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Suppose you need to know an equation of the tangent plane to a surface S at the point P(3, 1, 4). You don't have an equation for S but you know that the curves r1(t)= <3-3t, 1-t^2, -4t+t^2> and r2(u)= <2+u^2, 2u^3-1, 2u+2> both lie on S. Find an equation of the tangent plane at P.

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