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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

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

Increasing

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

Plug

x = - 1

into

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

Maximum (- 1, 2)

Plug

x = \frac{1}{3}

into

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

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

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

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