Chapter 9.4, Problem 45E

Find the domain of the function f(x) = x² – 1. In interval form, the domain of f is (-∞, 0). Find the domain of the function f(x) x + 1 2 – - x -3 -2 -1 1 2 x 2 (-0, 2) U (2, ∞0) 3.

1. (a) Draw the graphs of the functions x and x in the plane. Then find all integers n > 2 such that (0, 0) is an inflection point of the function f(x) = x". (x + 1)®x³(x – 2)ª(x – 4)³ for all x. Find all x (b) The second derivative f" of f is given by f"(x) corresponding to inflection points of the graph of f. (c) A polynomial function g has degree 18 (like the degree of f" in part (b)). What is the maximum number of inflection points that the graph of g could possibly have? Explain your answer. (d) From (a) - (c) we see that just because g"(c) = 0 does not mean that (c, g(c)) is an inflection point. What additional property must exist for (c, g(c)) to necessarily be an inflection point?