I'm working on a practice problem for my Calculus 3 course. It gives the function: $z=x^2+y^2$, and asks to graph the contours for $c=1,2,3$. Than asks to calculate the gradient at point $(2,1)$ and graph the result.
I'm fine with the first part. I'm letting z=c and solving for y, then graphing the result.It's the gradient portion I'm having issues with.
The gradient I came up with is: $\nabla(x^2+y^2)=\langle 2x,2y\rangle$, at $(2,1)$, = (4,2)
I'm not exactly sure how to graph this. Am I supposed to graph a line from $(2,1)$ to $(4,2)$ or what? Any help/explanation would be very much appreciated!