Let F(x, y, z)=2xy^2 +2yz^2 +2x^2z. (a) Find the directional derivative of F at the point...

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 the level 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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Expert Solution

milcah answered 1 year ago

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