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

The extreme f(x)=(x-1)^3(x-2)^2 is Saddle(1,0),Maximum(8/5 , 108/3125),Minimum(2,0)

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

extreme points

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

Saddle (1, 0), Maximum (\frac{8}{5}, \frac{108}{3125}), Minimum (2, 0)

Solution steps

f^{'} (x) = (x - 1)^{2} (x - 2) (5 x - 8)

Find intervals:

Increasing

: - \infty < x < 1,

Increasing

: 1 < x < \frac{8}{5},

Decreasing

: \frac{8}{5} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 1

into

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

Saddle (1, 0)

Plug

x = \frac{8}{5}

into

(x - 1)^{3} (x - 2)^{2} : \frac{108}{3125}

Maximum (\frac{8}{5}, \frac{108}{3125})

Plug

x = 2

into

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

Minimum (2, 0)

Saddle (1, 0), Maximum (\frac{8}{5}, \frac{108}{3125}), Minimum (2, 0)

f (x) = \frac{x}{ln ( x )}, 2 \leq x \leq 5

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

\frac{x}{x ^{2} + 12 x + 35}

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

f (x) = 2 x^{3} - 6 x + 1

What is the extreme f(x)=(x-1)^3(x-2)^2 ?
The extreme f(x)=(x-1)^3(x-2)^2 is Saddle(1,0),Maximum(8/5 , 108/3125),Minimum(2,0)