In Exercises 7377, we explore functions whose graphs approach a nonhorizontal line as x

Chapter 4, Problem 73

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In Exercises 7377, we explore functions whose graphs approach a nonhorizontal line as x . A line y = ax + b is called a slant asymptote if lim x(f (x) (ax + b)) = 0 or lim x(f (x) (ax + b)) = 0 73. Let f (x) = x2 x 1 (Figure 24). Verify the following: (a) f (0) is a local max and f (2) a local min. (b) f is concave down on (, 1) and concave up on (1,). (c) lim x1 f (x) = and lim x1+ f (x) = . (d) y = x + 1 is a slant asymptote of f as x . (e) The slant asymptote lies above the graph of f for x < 1 and below the graph for x > 1. y = x + 1 10 10 10 10 x y f(x) = x2 x 1