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

The extreme f(x)=x^3-x^2-x is Maximum(-1/3 , 5/27),Minimum(1,-1)

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

extreme points

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

Maximum (- \frac{1}{3}, \frac{5}{27}), Minimum (1, - 1)

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 : \frac{5}{27}

Maximum (- \frac{1}{3}, \frac{5}{27})

Plug

x = 1

into

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

Minimum (1, - 1)

Maximum (- \frac{1}{3}, \frac{5}{27}), Minimum (1, - 1)

What is the extreme f(x)=x^3-x^2-x ?
The extreme f(x)=x^3-x^2-x is Maximum(-1/3 , 5/27),Minimum(1,-1)