Constant-nth-Differences Proof Project: Let f(x) = ax3 + bx2 + cx + d. a. Find algebraically four consecutive values of f(x) for which the x-values are k units apart. That is, find f(x), f(x + k), f(x + 2k), and f(x + 3k). Expand the powers. b. Show that the third differences between the values in part a are independent of x and are equal to 6ak3. c. Let g(x) = 5x3 11x2 + 13x 19. Find g(3), g(10), g(17), g(24), and g(31). By finding the third differences between consecutive values, show numerically that the conclusion of part b is correct.

Lecture 22 Monday, October 12, 201512:04 PM PHCL 2600 Page 1 PHCL 2600 Page 2 PHCL 2600 Page 3 PHCL 2600 Page 4 PHCL 2600 Page 5 PHCL 2600 Page 6 Lecture 23 Tuesday, October 13, 20112:00 PM PHCL 2600 Page 1 PHCL 2600 Page 2 PHCL 2600 Page 3 PHCL 2600 Page 4 PHCL 2600 Page 5 PHCL 2600 Page 6 PHCL 2600 Page 7 Lecture 24 Wednesday, October 14, 20112:03 PM