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

The extreme f(x)=(x-1)^3(x+1)^3 is Saddle(-1,0),Minimum(0,-1),Saddle(1,0)

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

extreme points

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

Saddle (- 1, 0), Minimum (0, - 1), Saddle (1, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

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

Saddle (- 1, 0)

Plug

x = 0

into

(x - 1)^{3} (x + 1)^{3} : - 1

Minimum (0, - 1)

Plug

x = 1

into

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

Saddle (1, 0)

Saddle (- 1, 0), Minimum (0, - 1), Saddle (1, 0)

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

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

f (x) = 3 x^{4} - 8 x^{3}

f (x) = 3 x^{5} - 10 x^{3}

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

What is the extreme f(x)=(x-1)^3(x+1)^3 ?
The extreme f(x)=(x-1)^3(x+1)^3 is Saddle(-1,0),Minimum(0,-1),Saddle(1,0)