How to Approximate Partial Derivatives from Contour Map

Question

A problem of approximating partial derivatives from a given contour map Hi, I would like to know the connection between a contour map and partial derivatives. I understand that partial derivatives give a slope to the tangent line on a specific point but I cannot see the connection between it and a contour map

Answer 1

As the $z$ values are given, the contour map is a representation of a function $z=f(x,y)$. Hence graphical and numerical methods can be used to estimate the partial derivatives.

Answer 2

From what I can tell, only $c)$ has the numbers in the right places. For we do see that $f(1,1)=5$ and $f(-4,2)=0$. For instance, for $f_y$, we hold $x$ fixed, and vary $y$. Thus we get an estimate $f_y(1,1)=\dfrac{4-5}{1.25-1}$. We can see from the contours that, increasing $y$ a little at $(1,1)$, $z$ is about $4$. Etc