6. (a) Give the defnition of the directional derivative of f(x, y) at (a,b) in the direction of a unit vector u = (u,v), u2 + v2 = 1.

(13) A logistic population model with relative growth rate 0.1 per year and carrying capacity 50 thousand can be expressed by the differential equation =0.1P(1 - ), with P in thousands and t in years. Given that the initial population is 9 thousand. Find the population size after 20 years. (If you memorized the formula, then you need to derive it for this problem.)