What is the extreme f(x)=(x-2)^3(x-1) ?

The extreme f(x)=(x-2)^3(x-1) is Minimum(5/4 ,-27/256),Saddle(2,0)

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extreme f(x)=(x-2)^3(x-1)

extreme points

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

Minimum (\frac{5}{4}, - \frac{27}{256}), Saddle (2, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < \frac{5}{4},

Increasing

: \frac{5}{4} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = \frac{5}{4}

into

(x - 2)^{3} (x - 1) : - \frac{27}{256}

Minimum (\frac{5}{4}, - \frac{27}{256})

Plug

x = 2

into

(x - 2)^{3} (x - 1) : 0

Saddle (2, 0)

Minimum (\frac{5}{4}, - \frac{27}{256}), Saddle (2, 0)

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

f (x) = x^{\frac{1}{5}} (x + 3)

x^{3} + 3 x^{2} + 1

f (x) = - 5 x^{4} + 5 x^{3} - 10

f (x, y) = 3 x^{- 2} + 5 y^{- 2} + 8 x y^{2}

What is the extreme f(x)=(x-2)^3(x-1) ?
The extreme f(x)=(x-2)^3(x-1) is Minimum(5/4 ,-27/256),Saddle(2,0)