What is the extreme ((-6x+21))/(((x+1)^4)) ?

The extreme ((-6x+21))/(((x+1)^4)) is Minimum(5,-1/144)

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extreme ((-6x+21))/(((x+1)^4))

extreme points

\frac{( - 6 x + 21 )}{( ( x + 1 ) ^{4} )}

Minimum (5, - \frac{1}{144})

Solution steps

f^{'} (x) = - \frac{18 ( - x + 5 )}{( x + 1 ) ^{5}}

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 5

into

\frac{- 6 x + 21}{( x + 1 ) ^{4}} : - \frac{1}{144}

Minimum (5, - \frac{1}{144})

\frac{- 5}{4 x - 8}

f (x) = f (x) = x^{3} - 4 x^{2} - 3 x + 1

f (x) = x^{3} + 3 x^{2} - 189 x

f (x) = 1 - ∣ x - 7 ∣

f (x, y) = (x^{2} - 49)^{2} + (y^{2} - 9)^{2}

What is the extreme ((-6x+21))/(((x+1)^4)) ?
The extreme ((-6x+21))/(((x+1)^4)) is Minimum(5,-1/144)