A function f and a point P are given. Let θ correspond to the direction of the directional derivative. Complete parts (a) through (e).
f(x, y) = 16 - 4x² - 3y², P(-3,4)

(a) Find the gradient and evaluate it at P.
(b.1) What angle(s) is/are associated with the direction of maximum increase?
(b.2) What angle(s) is/are associated with the direction of maximum decrease?
(b.3) What angle(s) is/are associated with the direction of zero change?
(c) Write the directional derivative at P as a function of θ, call this function g(θ).
(d) Find the maximum value of g(θ). What value of θ maximizes g(θ)?
(e) Verify that the value of θ that maximizes g corresponds to the direction of the gradient. Verify that the maximum value of g equals the magnitude of the gradient. Are the values from part (d) consistent with the values from parts (a) and (b)?