Question

Partial Derivatives on Contour Maps:
What are the signs of partial derivatives with respect to x and y of points P,Q,R,S and why?
http://bit.ly/18Yct04

I'm not sure how to get these derivatives.

Answer 1

I know it's the picture is a picture of a depression in the ground, but how does one make the tangent lines?

Answer 2

I think, at P ( 8, pi/4), you have x = rcos theta, then dx/ dtheta= r sin theta, hence dx/dtheta = 4sqrt2

Answer 3

and the equation of the circle is F(x,y) = x^2 + y^2 -r^2, hence take partial derivative of them and put the part above in.

Answer 4

Ouch, that is a method, but it's unnecessarily tough.
I just learned one can increase x and y respectively and if the value increases, then the derivative is positive and vice-versa.

Thanks though!