Calculus 3:

Consider the function of temperature T(u; v) = uv^2

(a) Sketch 3 level curves of T including one that passes through the point (1; 1). Label the value of T on each level curve.

(b) If I start at the location (u; v)= (1; 1), give the unit vector associated with the direction (in the domain)Then sketch this vector at the point (1; 1) on your contour plot in part (a).

(c) What is the rate of change of the temperature in this direction?

(d) At the same location, give the unit vector(s) associated with the direction (in the domain)

(e) Use a directional derivative to estimate the change in temperature if I start at the point P0 = (1; 1) in the domain and move a distance of sqrt(0.5) miles toward the point P1 = (-1; 3).