A small aircraft starts its descent from an altitude of h = 2/3 mile, 4 miles west of the runway. Find the cubic f(x) = ax³ - bx² + cx - d on the interval that describes a smooth glide path for the landing.
a) Determine the values of coefficients a, b, c, and d.
b) Write the cubic function that represents the glide path.
c) Find the critical points of the function.
d) Calculate the area under the curve on the interval [-4, 0].