A plane is to take off and reach a level cruising altitude of h miles after a horizontal distance of 100 miles, as shown in the following diagram. Find a polynomial flight path of the form f(X) = aX3 + bx2 + cx + d by following steps (a) to (d) to determine the constants a, b, c, and d. (Assume h = 4 miles.) }I '_ height h slope zero ,1 height zero 510 >e zero _. x P 0 100 (D (a) Use the fact that the plane is on the ground at X = O [that is, f(0) = O] to determine the value of d. d = 0 / (b) Use the fact that the path is horizontal at X = O [that is, f'(0) = O] to determine the value of c. C=0 / (c) Use the fact that at X = 100 the height is 4 and the path is horizontal to determine the values of a and b. a: D: State the function f(X that you have determined. 1'00 =