Given f = ax? + x + y + xz2, where a is some constant parameter....

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Given f = ax? + x + y³ + xz2, where a is some constant parameter. %3D • Determine a = (positive integer), if the largest possible rate of change of f at point (1,0, 1)is given by 20- • Use the the value of a from the previous part. At which point (x, y, z) the directional derivative of f is zero in all directions? Give the values of x = (decimal), y = (integer) and z = (integer). • Determine a = (integer), if the Laplacian of fat point (1, 2, 1)is zero. Given f = ax? + x + y³ + xz2, where a is some constant parameter. %3D • Determine a = (positive integer), if the largest possible rate of change of f at point (1,0, 1)is given by 20- • Use the the value of a from the previous part. At which point (x, y, z) the directional derivative of f is zero in all directions? Give the values of x = (decimal), y = (integer) and z = (integer). • Determine a = (integer), if the Laplacian of fat point (1, 2, 1)is zero.