For each of the graphs below use the level curves of the fun

For each of the graphs below, use the level curves of the function z = f(x, y) to decide the sign (positive, negative, or zero) of each of the partial derivatives at the point P. Assume the x- and y-axes are in the usual positions.

Solution

fx(P) zero negative,since increasing x leads to lower contours fy(P) positive zero fxx(P) zero negative.The counters are getting closer ,so negative slopes are getting mor steep,so slopes are decreasing. fyy(P) positive,steeps are positive zero fxy(P) zero zero