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

The extreme f(x)=x^3-x^2-x-1 is Maximum(-1/3 ,-22/27),Minimum(1,-2)

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

extreme points

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

Maximum (- \frac{1}{3}, - \frac{22}{27}), Minimum (1, - 2)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Increasing

: 1 < x < \infty

Plug

x = - \frac{1}{3}

into

x^{3} - x^{2} - x - 1 : - \frac{22}{27}

Maximum (- \frac{1}{3}, - \frac{22}{27})

Plug

x = 1

into

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

Minimum (1, - 2)

Maximum (- \frac{1}{3}, - \frac{22}{27}), Minimum (1, - 2)

f (x) = 4 x y + 120 y - 20 y^{2} - \frac{1}{10} x^{2} y - 80

\frac{d}{d x} (x^{3} y^{2})

y = \frac{x ^{3}}{3} - x^{2} - 3 x

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

y = x^{2} + \frac{16}{x}

What is the extreme f(x)=x^3-x^2-x-1 ?
The extreme f(x)=x^3-x^2-x-1 is Maximum(-1/3 ,-22/27),Minimum(1,-2)