What is the critical ((2x^5-9x^3+8))/(-4x^2+6) ?

The critical ((2x^5-9x^3+8))/(-4x^2+6) is x=0,x\approx 0.44455…

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critical ((2x^5-9x^3+8))/(-4x^2+6)

critical points

\frac{( 2 x ^{5} - 9 x ^{3} + 8 )}{- 4 x ^{2} + 6}

x = 0, x \approx 0.44455 \dots

Solution steps

\frac{2 x ^{5} - 9 x ^{3} + 8}{- 4 x ^{2} + 6}

Find where

f^{'} (x)

is equal to zero or undefined

x = 0, x \approx 0.44455 \dots, x = - \frac{3}{2}, x = \frac{3}{2}

Identify critical points not in

f (x)

domain

Domain of

\frac{2 x ^{5} - 9 x ^{3} + 8}{- 4 x ^{2} + 6} : x < - \frac{3}{2} or - \frac{3}{2} < x < \frac{3}{2} or x > \frac{3}{2}

\frac{2 x ^{5} - 9 x ^{3} + 8}{- 4 x ^{2} + 6}

is not defined at

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

, therefore:

x = 0, x \approx 0.44455 \dots

f (x) = x^{\frac{1}{7}} + 5

2^{x}

x + \frac{32}{x ^{2}}

x^{2} y + x y^{2} + 3 x y

x - \frac{1}{x}

What is the critical ((2x^5-9x^3+8))/(-4x^2+6) ?
The critical ((2x^5-9x^3+8))/(-4x^2+6) is x=0,x\approx 0.44455…