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

The extreme f(x)=(x^2-1)^3 is Saddle(-1,0),Minimum(0,-1),Saddle(1,0)

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

extreme points

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

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

Solution steps

f^{'} (x) = 6 x (x^{2} - 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^{2} - 1)^{3} : 0

Saddle (- 1, 0)

Plug

x = 0

into

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

Minimum (0, - 1)

Plug

x = 1

into

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

Saddle (1, 0)

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

1

x^{5} - 5 x

\frac{( x + 3 ) ( x - 3 )}{x ^{2} + 9}

cos (\frac{x}{4} + \frac{π}{4}) - 2

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