Chapter 3.3, Problem 24E

Find the directional derivative of the function at P in the direction of V. f(x,y) = x³-y³, P(5,4), v = √² (i+j) a. (922.5)√√2 b. (-5.252.5)√√2 D C. (1,845.0)√√2 d. (5,252.5)√2 e. (1,677.5)√√2

Find the directional derivative of f(x, y, z) = xy + z³ at the point P = (3, −4, −3) in the direction pointing to the origin. (Give an exact answer. Use symbolic notation and fractions where needed.) Dof(P) =

Consider the following function which is defined for all x and y: f(x, y) = 2(1-p²)x²y² - x² - y² + 3pxy + 2x+4y+2 where p is a constant. (a) Find the first order derivatives of f and enter them as functions of x, y and p (b) Find the second order derivatives of f and enter them as functions of x, y and p (c) For p = 1, find the stationary point (x*, y*).