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

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

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

extreme points

\frac{x}{x ^{2} - 6 x + 8}

Minimum (- 22, - \frac{3 - 2 2}{2}), Maximum (22, - \frac{2 2 + 3}{2})

Solution steps

f^{'} (x) = \frac{- x ^{2} + 8}{( x ^{2} - 6 x + 8 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 22,

Increasing

: - 22 < x < 2,

Increasing

: 2 < x < 22,

Decreasing

: 22 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 22

into

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

Minimum (- 22, - \frac{3 - 2 2}{2})

Plug

x = 22

into

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

Maximum (22, - \frac{2 2 + 3}{2})

Minimum (- 22, - \frac{3 - 2 2}{2}), Maximum (22, - \frac{2 2 + 3}{2})

f (x) = \frac{9 x ( x - 7 )}{2 x ^{2} - 5 x - 3}

f (x) = x^{3} - 3 x^{2} - 3 x + 5

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

f (x) = 3 - (x + 12.2)^{2} - 3

x^{3} + 8

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