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

The extreme f(x)=x^3-x^2-x-2 is Maximum(-1/3 ,-49/27),Minimum(1,-3)

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

extreme points

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

Maximum (- \frac{1}{3}, - \frac{49}{27}), Minimum (1, - 3)

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 - 2 : - \frac{49}{27}

Maximum (- \frac{1}{3}, - \frac{49}{27})

Plug

x = 1

into

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

Minimum (1, - 3)

Maximum (- \frac{1}{3}, - \frac{49}{27}), Minimum (1, - 3)

f (x) = 6 x - 1

f (x) = \frac{3 - x}{4}

x^{3} - 3 x^{2} - 8 x + 160

f (x) = 6 x ∣ x ∣

\frac{2 x + 4}{x}

What is the extreme f(x)=x^3-x^2-x-2 ?
The extreme f(x)=x^3-x^2-x-2 is Maximum(-1/3 ,-49/27),Minimum(1,-3)