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 , 59/27),Minimum(1,1)

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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{59}{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 + 2 : \frac{59}{27}

Maximum (- \frac{1}{3}, \frac{59}{27})

Plug

x = 1

into

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

Minimum (1, 1)

Maximum (- \frac{1}{3}, \frac{59}{27}), Minimum (1, 1)

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

f (x) = - \frac{1}{9} x + \frac{4}{3}

g (x) = 2 x - 1

(8, - 8.5), (8, - 6)

f (x) = \frac{( 1 + x ^{2} )}{( 2 + x ^{4} )}

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 , 59/27),Minimum(1,1)