Question: 9. Let F(x, y, z) = 23 + 3xyz - 2z2 a. Calculate the gradient of F. b. Find the directional derivative of F at

9. Let F(x, y, z) = 23 + 3xyz - 2z2

9. Let F(x, y, z) = 23 + 3xyz - 2z2 a. Calculate the gradient of F. b. Find the directional derivative of F at the point (2, 0, -1) in the direction of the vector (2, 1, -2). c. Find an equation for the tangent plane to the surface F(x, y, z) = 6 at (2, 0, -1). d. It is given that the equation x3 + 3xyz - 2z2 = 6 defines x implicitly in terms of y and z near (2, 0, -1). Calculate x (2, 0, -1)

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