How do I accurately visualize and describe level curves?
For the 14.1 homework tonight, many of the problems ask you to describe the level curves of the function. I understand how to do the rest of the problem, but how does one visualize what the level curves will look like? Is a 3D graphing program necessary, or is it possible to look at the function and tell?
For example (Exercise 14.1.1), let $ f(x,y) = (x−y)^2$. The level curves of this function looks like lines of slope $1$... how could one tell that from the function alone?
Comment: We haven't covered level curves in class, but they will be major when we get back after the fourth of July!!