A small aircraft starts its descent from an altitude of h = 1.4 miles, 4 miles west of the runway a. Find the cubic f(x)=ax3+bx2+cx+d on the interval [−4,0] that describes a smooth glide path for the landing.
b. The function in part (a) models the glide path of the plane. When would the plane be descending at the greatest rate?

Step-by-step explanation:

From the question we are told that

Altitude of Height 1.4miles

4miles west

a) From the question

on interval (-4,0)

The descent can be expressed in

therefore  initial points is (-4 , 1.4).

final co-ordinate is given by (0,0) as its landing

Mathematically solving in above  cubic equation

Generally in this case Slope of tangent at point of descent is zero.assuming flight was initially straight before descent

Mathematically solving above equations we have

Therefore having found a and b the Cubic equation is given as

b)descent at its greatest rate