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

The extreme f(x)=(x+1)^3(x-1) is Saddle(-1,0),Minimum(1/2 ,-27/16)

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

extreme

Saddle (- 1, 0), Minimum (\frac{1}{2}, - \frac{27}{16})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Decreasing

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

Increasing

: \frac{1}{2} < x < \infty

Plug

x = - 1

into

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

Saddle (- 1, 0)

Plug

x = \frac{1}{2}

into

(x + 1)^{3} (x - 1) : - \frac{27}{16}

Minimum (\frac{1}{2}, - \frac{27}{16})

Saddle (- 1, 0), Minimum (\frac{1}{2}, - \frac{27}{16})

What is the extreme f(x)=(x+1)^3(x-1) ?
The extreme f(x)=(x+1)^3(x-1) is Saddle(-1,0),Minimum(1/2 ,-27/16)