Question

Arthur

偏導數計算

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4. (C) 假設f(x,y,z)和g(x,y,z)有連續的偏導數,還有點 P = (1,2,-1)位於曲面上
f(x,y,z)=3上。已知:
Assume f(x,y,z) and g(x, y, z) have continuous partial derivatives and the point P =
(1, 2, -1) lies on the level surface f(x, y, z) = 3. You are given that
• The tangent plane (to ten) of f(x, y, z) = 3 at P is 2x – y + 3z = -3
• fy(1,2, -1) = 2
(a) Find & vf(1, 2, -1).
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(b)使用 P處的線性迫近來估計f(1.1, 2.01, -0.98)。
Estimate the value of f(1.1, 2.01, -0.98) by the linearization of f at P.