What is the critical 2x+(4x)/(3x-1) ?

The critical 2x+(4x)/(3x-1) is x=(-sqrt(2)+1)/3 ,x=(sqrt(2)+1)/3

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critical 2x+(4x)/(3x-1)

critical points

2 x + \frac{4 x}{3 x - 1}

x = \frac{- 2 + 1}{3}, x = \frac{2 + 1}{3}

Solution steps

2 x + \frac{4 x}{3 x - 1}

Find where

f^{'} (x)

is equal to zero or undefined

x = \frac{- 2 + 1}{3}, x = \frac{2 + 1}{3}, x = \frac{1}{3}

Identify critical points not in

f (x)

domain

Domain of

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

2 x + \frac{4 x}{3 x - 1}

is not defined at

x = \frac{1}{3}

, therefore:

x = \frac{- 2 + 1}{3}, x = \frac{2 + 1}{3}

f (x) = x^{2} - 4

3 sin (2 x - \frac{π}{4}) + 1

(4, - 3), (- 1, 3)

f (x) = \frac{4 x - 1}{2 x + 7}

f (x) = \frac{( 7 - 4 x )}{7 + 5 x}

What is the critical 2x+(4x)/(3x-1) ?
The critical 2x+(4x)/(3x-1) is x=(-sqrt(2)+1)/3 ,x=(sqrt(2)+1)/3