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

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

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

extreme points

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

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

Maximum (- 1, 1)

Plug

x = \frac{1}{3}

into

x^{3} + x^{2} - x : - \frac{5}{27}

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

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

f (x, y) = x - 9 y + 17

\frac{x ^{2} - 2 x + 2}{x - 1}

f (x, y) = y^{3} + x^{2} - 6 x y + 3 x + 6 y - 7

f (x, y) = - x^{4} - y^{4} + 4 x y

x^{2} - 4

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