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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Increasing

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

Decreasing

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

Increasing

: 0 < x < \infty

Plug

x = - 1

into

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

Saddle (- 1, 0)

Plug

x = - \frac{2}{5}

into

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

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

Plug

x = 0

into

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

Minimum (0, 0)

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

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

f (x, y) = 4 x^{2} + 2 y^{2} - 2 x y - 10 y - 2 x

f (x) = (x + 2)^{2}

f (x) = cos^{2} (x) - 2 sin (x)

f (x) = \frac{x}{x ^{2} + 1}, 0 \leq x \leq 2

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