Been struggling with this problem. It seems like C is at (6,5) and A is at (2,4) so when I subtract them to find the (delta) or average rate of change I get $\frac{1}{4}$. But it isn't the right answer. What's my problem here?
How to find the average rate of change of two points in a contour map
calculusmultivariable-calculus
Best Answer
The distance between $A$ and $C$ is to be calculated by the Pythagoras theorem. The changein the value of the fiwld is to be read from the diagram to be $\phi_C - \phi_A =-2a$. The average rate of change is then $$ \Delta=\frac{2a}{\sqrt{4^2+1}} = a\frac{2}{\sqrt{17}} $$ $$ a = -14 \implies \Delta = -14\frac{2}{\sqrt{17}} = -\frac{28}{\sqrt{17}} $$