0
$\begingroup$

I am comparing the gradient to directional derivative and would like to know if the gradient in this two dimensional model lies on the x , y plane only or on and infinite number of parallel horizontal planes over the x, y plane.

Maybe I better use and example ...lets's use z = f( x, y ) = x^2 + y^2.

$\endgroup$
1
$\begingroup$

Yes of course, the gradient is a vector which lies in the $x-y$ plane that is for your example

$$\nabla f=(f_x,f_y)=(2x,2y)$$

Note that it represents geometrically the direction with maximum slope of the graph $z=f(x,y)$ and the maximum slope is given by the norm i.e."lenght of the gradient" vector.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.