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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 8E
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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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