Constant-nth-Differences Proof Project: Let f(x) = ax3 + bx2 + cx + d. a. Find
Chapter 15, Problem 12(choose chapter or problem)
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.
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