Quiz 4 level curves are shown for a function f determine

Question

Quiz 4 - Math 53, section 213

1. Level curves are shown for a function f. Determine whether the following partial derivatives are positive or negative at the point P.

(a) f_x

(b) f_y

(c) f_xx

(d) f_xy

(e) f_yy

2. If z = f(x, y) where f is differentiable, and x = g(t), y = h(t), g(3) = 2, h(3) = 7, g'(3) = 5, h'(3) = -4, f_x(2, 7) = 6, and f_y(2, 7) = 8, find dz/dt, when t = 3.