Question: Let f ( x , y , z ) = x 2 y e - z , u = 1 , 1 , - 1

Let f(x,y,z)=x2ye-z,u=1,1,-1> and P0=(1,1,0). Find
(a) the gradient vector of f at P0;
(b) the derivative of f at P0 in the direction of u;
(c) directions in which f changes most rapidly at P0, and the rates of change in these directions;
(d) direction in which f does not change at P0.
Let f ( x , y , z ) = x 2 y e - z , u = < 1 , 1 ,

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