What is the extreme ((x-2)^3)/((x-4)^4) ?

The extreme ((x-2)^3)/((x-4)^4) is Minimum(-4,-27/512),Saddle(2,0)

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extreme ((x-2)^3)/((x-4)^4)

extreme points

\frac{( x - 2 ) ^{3}}{( x - 4 ) ^{4}}

Minimum (- 4, - \frac{27}{512}), Saddle (2, 0)

Solution steps

f^{'} (x) = \frac{( x - 2 ) ^{2} ( - x - 4 )}{( x - 4 ) ^{5}}

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 2,

Increasing

: 2 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 4

into

\frac{( x - 2 ) ^{3}}{( x - 4 ) ^{4}} : - \frac{27}{512}

Minimum (- 4, - \frac{27}{512})

Plug

x = 2

into

\frac{( x - 2 ) ^{3}}{( x - 4 ) ^{4}} : 0

Saddle (2, 0)

Minimum (- 4, - \frac{27}{512}), Saddle (2, 0)

f (x) = \frac{4 x ^{2}}{x - 2}, - 2 \leq x \leq 1

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

f (x) = (x - 6)^{\frac{2}{3}}

\frac{x ^{2} + 2}{7 x - 4 x ^{2}}

f (x) = - 10 x^{2} + 1620 x - 40000

What is the extreme ((x-2)^3)/((x-4)^4) ?
The extreme ((x-2)^3)/((x-4)^4) is Minimum(-4,-27/512),Saddle(2,0)