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

The extreme f(x)=x^3(x-2)^2 is Saddle(0,0),Maximum(6/5 , 3456/3125),Minimum(2,0)

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

extreme points

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

Saddle (0, 0), Maximum (\frac{6}{5}, \frac{3456}{3125}), Minimum (2, 0)

Solution steps

f^{'} (x) = x^{2} (x - 2) (5 x - 6)

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{6}{5},

Decreasing

: \frac{6}{5} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = \frac{6}{5}

into

x^{3} (x - 2)^{2} : \frac{3456}{3125}

Maximum (\frac{6}{5}, \frac{3456}{3125})

Plug

x = 2

into

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

Minimum (2, 0)

Saddle (0, 0), Maximum (\frac{6}{5}, \frac{3456}{3125}), Minimum (2, 0)

x^{3} e^{- x}

f (x, y) = x ln (x^{2} + y^{2})

f (x) = x^{\frac{12}{5}} - 6 x^{\frac{2}{5}} + 2

10 x - 5 x ln (x)

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

What is the extreme f(x)=x^3(x-2)^2 ?
The extreme f(x)=x^3(x-2)^2 is Saddle(0,0),Maximum(6/5 , 3456/3125),Minimum(2,0)