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

The extreme f(x)=x^3+x^2-x-1 is Maximum(-1,0),Minimum(1/3 ,-32/27)

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

extreme points

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

Maximum (- 1, 0), Minimum (\frac{1}{3}, - \frac{32}{27})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \infty

Plug

x = - 1

into

x^{3} + x^{2} - x - 1 : 0

Maximum (- 1, 0)

Plug

x = \frac{1}{3}

into

x^{3} + x^{2} - x - 1 : - \frac{32}{27}

Minimum (\frac{1}{3}, - \frac{32}{27})

Maximum (- 1, 0), Minimum (\frac{1}{3}, - \frac{32}{27})

f (x) = (x^{2} + 10) (9 - x^{2})

\frac{2 x}{x ^{2} - 4}

f (x, y) = 3 x^{4} + 3 y^{4} - x y

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

f (x) = 2 x - 5 x^{2} - 2 x y - 3 y^{2} + 3 y

What is the extreme f(x)=x^3+x^2-x-1 ?
The extreme f(x)=x^3+x^2-x-1 is Maximum(-1,0),Minimum(1/3 ,-32/27)