What is the critical (x^2+4x+3)/(x^3-2x^2-5x+6) ?

The critical (x^2+4x+3)/(x^3-2x^2-5x+6) is x\approx-6.69935…,x\approx 1.85470…

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critical (x^2+4x+3)/(x^3-2x^2-5x+6)

critical points

\frac{x ^{2} + 4 x + 3}{x ^{3} - 2 x ^{2} - 5 x + 6}

x \approx - 6.69935 \dots, x \approx 1.85470 \dots

Solution steps

\frac{x ^{2} + 4 x + 3}{x ^{3} - 2 x ^{2} - 5 x + 6}

Find where

f^{'} (x)

is equal to zero or undefined

x \approx - 6.69935 \dots, x \approx 1.85470 \dots, x = - 2, x = 1, x = 3

Identify critical points not in

f (x)

domain

Domain of

\frac{x ^{2} + 4 x + 3}{x ^{3} - 2 x ^{2} - 5 x + 6} : x < - 2 or - 2 < x < 1 or 1 < x < 3 or x > 3

\frac{x ^{2} + 4 x + 3}{x ^{3} - 2 x ^{2} - 5 x + 6}

is not defined at

x = - 2, x = 1, x = 3

, therefore:

x \approx - 6.69935 \dots, x \approx 1.85470 \dots

What is the critical (x^2+4x+3)/(x^3-2x^2-5x+6) ?
The critical (x^2+4x+3)/(x^3-2x^2-5x+6) is x\approx-6.69935…,x\approx 1.85470…