Question

If (x,y,z)=3x²y-yz?, find grad at point (2,2,-1)

Answer 1

By definition, a gradient of a function $f$ is a vector function given by $\nabla f (x,y,z) = (\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z})$. Let us calculate each of partial derivatives :

$\frac{\partial f}{\partial x} = 6xy, \: \frac{\partial f}{\partial y}=3x^2-z, \: \frac{\partial f}{\partial z}=-y$

Putting $(x,y,z)=(2,2,-1)$ gives us a vector $(24, 13, -2)$.