What is the extreme ((-x^2-8x+20))/((x^2-5x)^2) ?

The extreme ((-x^2-8x+20))/((x^2-5x)^2) is Minimum(-16.10976…,-0.00095…)

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extreme ((-x^2-8x+20))/((x^2-5x)^2)

extreme points

\frac{( - x ^{2} - 8 x + 20 )}{( x ^{2} - 5 x ) ^{2}}

Minimum (- 16.10976 \dots, - 0.00095 \dots)

Solution steps

Find the critical points:

x \approx - 16.10976 \dots

Domain of

\frac{- x ^{2} - 8 x + 20}{( x ^{2} - 5 x ) ^{2}} : x < 0 or 0 < x < 5 or x > 5

Find intervals:

Decreasing

: - \infty < x < - 16.10976 \dots,

Increasing

: - 16.10976 \dots < x < 0,

Decreasing

: 0 < x < 5,

Increasing

: 5 < x < \infty

Plug the extreme point

x = - 16.10976 \dots

into

\frac{- x ^{2} - 8 x + 20}{( x ^{2} - 5 x ) ^{2}} \Rightarrow y = - 0.00095 \dots

Minimum (- 16.10976 \dots, - 0.00095 \dots)

f (x) = 2 x^{2} + 1

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

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

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

x^{\frac{1}{9}} + 1

What is the extreme ((-x^2-8x+20))/((x^2-5x)^2) ?
The extreme ((-x^2-8x+20))/((x^2-5x)^2) is Minimum(-16.10976…,-0.00095…)