Question

Suppose that ( f(x, y, z)=x^{2} y z-x y z^{3} ) is a function of three variables. 1. Find the gradient of ( f(x, y, z) ). Answer: ( abla f(x, y, z)= ) 2. Evaluate the gradient at the point ( P(2,-2,2) ). Answer: ( abla f(2,-2,2)= ) 3. Find the rate of change of ( f(x, y, z) ) at ( P ) in the direction of the vector ( mathbf{u}=leftlangle 0, frac{4}{5},-frac{3}{5} ight angle ). Answer: ( D_{mathbf{u}} f(2,-2,2)= )

          Suppose that ( f(x, y, z)=x^{2} y z-x y z^{3} ) is a function of three variables.
1. Find the gradient of ( f(x, y, z) ).
Answer: ( 
abla f(x, y, z)= )
2. Evaluate the gradient at the point ( P(2,-2,2) ).
Answer: ( 
abla f(2,-2,2)= )
3. Find the rate of change of ( f(x, y, z) ) at ( P ) in the direction of the vector ( mathbf{u}=leftlangle 0, frac{4}{5},-frac{3}{5}
ight
angle ).
Answer: ( D_{mathbf{u}} f(2,-2,2)= )

$Suppose that ( f(x, y, z)=x^2 y z-x y z^3 ) is a function of three variables. 1. Find the gradient of ( f(x, y, z) ). Answer: ( abla f(x, y, z)= ) 2. Evaluate the gradient at the point ( P(2,-2,2) ). Answer: ( abla f(2,-2,2)= ) 3. Find the rate of change of ( f(x, y, z) ) at ( P ) in the direction of the vector ( mathbfu=leftlangle 0, frac45,-frac35 ight angle ). Answer: ( Dmathbfu f(2,-2,2)= )$

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