1. Find grad f for f(r)=xyz at the point (1, 2, 3). Hence calculate (a) the...

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1. Find grad f for f(r)=x²yz² at the point (1, 2, 3). Hence calculate (a) the directional derivative of f(r) at (1, 2, 3) in the direction of the vector (-2, 3, -6); 3. (b) the maximum rate of change of the function at (1, 2, 3) and its direction. 2. Find Vf where f(r) is (a) x² + y²-z (b) z tan¹ (y/x) (c) e-*-+²/√(x³ + y²) (d) xyz sin {(x+y+z)} Find the directional derivative of f(r) = x² + y² − z at the point (1, 1, 2) in the direction of the vector (4, 4,-2). 1. Find grad f for f(r)=x²yz² at the point (1, 2, 3). Hence calculate (a) the directional derivative of f(r) at (1, 2, 3) in the direction of the vector (-2, 3, -6); 3. (b) the maximum rate of change of the function at (1, 2, 3) and its direction. 2. Find Vf where f(r) is (a) x² + y²-z (b) z tan¹ (y/x) (c) e-*-+²/√(x³ + y²) (d) xyz sin {(x+y+z)} Find the directional derivative of f(r) = x² + y² − z at the point (1, 1, 2) in the direction of the vector (4, 4,-2).