Let F(x, y, z)=2xy^2 +2yz^2 +2x^2z. (a) Find the directional derivative of F at the point...
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Let F(x, y, z)=2xy^2 +2yz^2 +2x^2z.
(a) Find the directional derivative of F at the point (−2, 1,−1) in the direction parallel to the line x = 3 + 4t, y = 2 − t, z= 3t.
Answer: 58/√26
(b) Determine symmetric equations for the normal line to thelevel surface F(x, y, z)= −2 at the point (−1, 2, 1).
Answer: x = −1 + 4t, y = 2 − 6t, z = 1 + 10t
Let F(x, y, z)=2xy^2 +2yz^2 +2x^2z.
(a) Find the directional derivative of F at the point (−2, 1,−1) in the direction parallel to the line x = 3 + 4t, y = 2 − t, z= 3t.
Answer: 58/√26
(b) Determine symmetric equations for the normal line to thelevel surface F(x, y, z)= −2 at the point (−1, 2, 1).
Answer: x = −1 + 4t, y = 2 − 6t, z = 1 + 10t
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