Let f (x, y, z) = xy - xyz + z. (a) What is the maximum...

  

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Let f (x, y, z) = xy² - xyz + z³. (a) What is the maximum rate of increase of the function at the point (1,2,1), and in which direction does it occur? (b) Find the directional derivative of the function f at the point (1,2,1) in the direction with direction angles 60°, 45° and 60°. Q4)(20 points) Find the plane tangent at the point (2,3,-1) to the surface defined implicitly by the equation In(xy + x2 + yz) = 0 assuming z = f(x,y) is a differentiable function of x and y in some neighborhood of the point (2,3). and z = -1 when x = 2 and y = 3. Let f (x, y, z) = xy² - xyz + z³. (a) What is the maximum rate of increase of the function at the point (1,2,1), and in which direction does it occur? (b) Find the directional derivative of the function f at the point (1,2,1) in the direction with direction angles 60°, 45° and 60°. Q4)(20 points) Find the plane tangent at the point (2,3,-1) to the surface defined implicitly by the equation In(xy + x2 + yz) = 0 assuming z = f(x,y) is a differentiable function of x and y in some neighborhood of the point (2,3). and z = -1 when x = 2 and y = 3.

Answer rating: 100% (QA)

To solve this problem well start by calculating the gradient of the function fx y z xy xyz z The gra... View the full answer