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

The extreme f(x)=(x-1)^3(x-2) is Saddle(1,0),Minimum(7/4 ,-27/256)

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

extreme points

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

Saddle (1, 0), Minimum (\frac{7}{4}, - \frac{27}{256})

Solution steps

f^{'} (x) = (x - 1)^{2} (4 x - 7)

Find intervals:

Decreasing

: - \infty < x < 1,

Decreasing

: 1 < x < \frac{7}{4},

Increasing

: \frac{7}{4} < x < \infty

Plug

x = 1

into

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

Saddle (1, 0)

Plug

x = \frac{7}{4}

into

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

Minimum (\frac{7}{4}, - \frac{27}{256})

Saddle (1, 0), Minimum (\frac{7}{4}, - \frac{27}{256})

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

f (x) = - x^{3} + 27 x - 51

f (x) = - x^{3} + 27 x - 63

f (x) = 3 x^{2} - 9 y^{2}

f (x, y) = 4 - x^{2} - 2 y^{2}

What is the extreme f(x)=(x-1)^3(x-2) ?
The extreme f(x)=(x-1)^3(x-2) is Saddle(1,0),Minimum(7/4 ,-27/256)