What is the extreme y=x^3-x^2-x+1 ?

The extreme y=x^3-x^2-x+1 is Maximum(-1/3 , 32/27),Minimum(1,0)

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extreme y=x^3-x^2-x+1

extreme points

y = 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)

y = 1 x^{2} + 4 x + 4

f (x) = x^{2} - 4 x + 5, x \leq 2

f (x) = 7 x + 3

f (x) = x + 7 + 5

What is the extreme y=x^3-x^2-x+1 ?
The extreme y=x^3-x^2-x+1 is Maximum(-1/3 , 32/27),Minimum(1,0)