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 , 32/27),Minimum(1,0)

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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{32}{27}), Minimum (1, 0)

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{32}{27}

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

Plug

x = 1

into

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

Minimum (1, 0)

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

f (x) = \frac{x ^{2}}{1 + x}

f (x) = 3 (x + 2)^{2} - 7

f (x) = 2 x^{3} - 24 x^{2} + 72 x

x^{2} - 8 x - 5

\frac{7 x}{x + 4}

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 , 32/27),Minimum(1,0)