What is the extreme-(6x)/(6x^2+8) ?

The extreme-(6x)/(6x^2+8) is Maximum(-2/(sqrt(3)),(sqrt(3))/4),Minimum(2/(sqrt(3)),-(sqrt(3))/4)

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extreme-(6x)/(6x^2+8)

extreme

Maximum (- \frac{2}{3}, \frac{3}{4}), Minimum (\frac{2}{3}, - \frac{3}{4})

Solution steps

f^{'} (x) = - \frac{3 ( - 3 x ^{2} + 4 )}{( 3 x ^{2} + 4 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3},

Decreasing

: - \frac{2}{3} < x < \frac{2}{3},

Increasing

: \frac{2}{3} < x < \infty

Plug

x = - \frac{2}{3}

into

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

Maximum (- \frac{2}{3}, \frac{3}{4})

Plug

x = \frac{2}{3}

into

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

Minimum (\frac{2}{3}, - \frac{3}{4})

Maximum (- \frac{2}{3}, \frac{3}{4}), Minimum (\frac{2}{3}, - \frac{3}{4})

What is the extreme-(6x)/(6x^2+8) ?
The extreme-(6x)/(6x^2+8) is Maximum(-2/(sqrt(3)),(sqrt(3))/4),Minimum(2/(sqrt(3)),-(sqrt(3))/4)