What is the critical f(x)=(x+1)/(-x^3+3x^2+x-3)+3 ?

The critical f(x)=(x+1)/(-x^3+3x^2+x-3)+3 is x=2

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critical f(x)=(x+1)/(-x^3+3x^2+x-3)+3

critical points

f (x) = \frac{x + 1}{- x ^{3} + 3 x ^{2} + x - 3} + 3

x = 2

Solution steps

\frac{x + 1}{- x ^{3} + 3 x ^{2} + x - 3} + 3

Find where

f^{'} (x)

is equal to zero or undefined

x = 2, x = 1, x = 3

Identify critical points not in

f (x)

domain

Domain of

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

\frac{x + 1}{- x ^{3} + 3 x ^{2} + x - 3} + 3

is not defined at

x = 1, x = 3

, therefore:

x = 2

f (x) = x^{4} + x^{2} + 3

x^{2} y - x y^{2}

f (x) = \frac{x}{x ^{2} + 12 x + 32}

y = 2 x + 3

f (θ) = 10 cos (θ) + 5 sin^{2} (θ)

What is the critical f(x)=(x+1)/(-x^3+3x^2+x-3)+3 ?
The critical f(x)=(x+1)/(-x^3+3x^2+x-3)+3 is x=2