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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

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

Increasing

: \frac{2}{5} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = \frac{2}{5}

into

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

Minimum (\frac{2}{5}, - \frac{108}{3125})

Plug

x = 1

into

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

Saddle (1, 0)

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

3 - 2 x - x^{2}

y = 2 x + 1

y = ∣ x - 3 ∣

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

(- 6, - 2), (- 4, 0)

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