Chapter 4.2, Problem 62E

5. Use the function f(x) = x³ + 2x² + x - 2, create a table with 8 inputs and outputs. Complete the triangular differences until you have a common difference. Lastly explain what the result reveals.

A basketball player makes a successful shot from the free throw line. Suppose that the path of the ball from the moment of release to the moment it enters the hoop is described by y = 2.07 + 2.15x – 0.49x?,0 < x< 4.6 where x is the horizontal distance (in meters) from the point of release, and y is the vertical distance (in meters) above the floor. Use a CAS or a scientific calculator with a numerical integration capability to approximate the distance the ball travels from the moment it is released to the moment it enters the hoop. Round your answer to two decimal places. D = i

Please select the correct answer and explain in detail your reasoning.