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I think my derivation is wrong because I can’t find the critical points (I’m getting complex numbers instead of real numbers) can you show me how to derive this and get critical points

I think my derivation is wrong because I can’t find the critical points (I’m getting complex numbers instead of real numbers) can you show me how to derive this and get critical points

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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I think my derivation is wrong because I can’t find the critical points (I’m getting complex numbers instead of real numbers) can you show me how to derive this and get critical points
f(x)=2x-11-x²+2x 2-x (1) dom f=\{2} asymptotes: lim f(x) = +os, lim f(x) = -00 8448 8154 (17) f(x) = I lim_ f(x) = +∞0₁ 2-2 2(x-1)-x²+2x 2-x 2-2+ -x²+4x-2 2-2 2(-x+1)=x²+2x = -2²-2 2-x 2-2 -2²-2 2-2 = -∞0 ⇒x=2 is a vertical asymptote -x² +42-2 → (-2x+4)(2-x) − (−x²+4x−2)(-1) = x²-4x+b ⇒>> 2-2 (2-x)² (2-2)² (-22) (2-2) - (-2²-2)(-1) →> (2-2)² - x²-4x-2 (2-2)²
Transcribed Image Text:f(x)=2x-11-x²+2x 2-x (1) dom f=\{2} asymptotes: lim f(x) = +os, lim f(x) = -00 8448 8154 (17) f(x) = I lim_ f(x) = +∞0₁ 2-2 2(x-1)-x²+2x 2-x 2-2+ -x²+4x-2 2-2 2(-x+1)=x²+2x = -2²-2 2-x 2-2 -2²-2 2-2 = -∞0 ⇒x=2 is a vertical asymptote -x² +42-2 → (-2x+4)(2-x) − (−x²+4x−2)(-1) = x²-4x+b ⇒>> 2-2 (2-x)² (2-2)² (-22) (2-2) - (-2²-2)(-1) →> (2-2)² - x²-4x-2 (2-2)²
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