The following is a contour map for the function fxy Determin

The following is a contour map for the function f(x,y). Determine the signs of f_x , f_y, f_xx, f_yy, and f_yx at the point P. Justify your answer.

in determinated Steinmeier Prime Ministry an online 3

Solution

a.Moving to the right leads to higher contours. Therefore fx(P) is positive.

b.Moving upwards in y leads to decrease in contours. Therefore fy(P) is negative.

c.fxx(P) is positive. x slope is positive (from (a)), and because the contours are getting closer, the positive slopes are getting steeper, so the slopes are increasing.

d.fyy(P) is positive. Slopes are negative, but getting less steep as we move upwards in y.

e.fyx(P) is negative. Consider either x slopes, which are positive, get flatter as you move upwards, or the y slopes, which are negative, get steeper as you move to the right.