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x² 1) Let f(x): = (Figure 24). Verify the following: x - 1 (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 f(x) = = -∞ and lim f(x) = ∞. x→1- x→1+ (d) y = x + 1 is a slant asymptote of f(x) as x → ∞o. (e) The slant asymptote lies above the graph of f(x) for x < 1 and below the graph for x > 1. y x² | || f(x) =

x² 1) Let f(x): = (Figure 24). Verify the following: x - 1 (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 f(x) = = -∞ and lim f(x) = ∞. x→1- x→1+ (d) y = x + 1 is a slant asymptote of f(x) as x → ∞o. (e) The slant asymptote lies above the graph of f(x) for x < 1 and below the graph for x > 1. y x² | || f(x) =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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x² 1) Let f(x): = (Figure 24). Verify the following: x - 1 (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 f(x) = = -∞ and lim f(x) = ∞. x→1- x→1+ (d) y = x + 1 is a slant asymptote of f(x) as x → ∞o. (e) The slant asymptote lies above the graph of f(x) for x < 1 and below the graph for x > 1. y f(x) = -10 10 -10 FIGURE 24 y=x+1 10 X
Transcribed Image Text:x² 1) Let f(x): = (Figure 24). Verify the following: x - 1 (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 f(x) = = -∞ and lim f(x) = ∞. x→1- x→1+ (d) y = x + 1 is a slant asymptote of f(x) as x → ∞o. (e) The slant asymptote lies above the graph of f(x) for x < 1 and below the graph for x > 1. y f(x) = -10 10 -10 FIGURE 24 y=x+1 10 X
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