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

The extreme f(x)=x^3-2x^2+x+1 is Maximum(1/3 , 31/27),Minimum(1,1)

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

extreme points

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

Maximum (\frac{1}{3}, \frac{31}{27}), Minimum (1, 1)

Solution steps

f^{'} (x) = 3 x^{2} - 4 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} - 2 x^{2} + x + 1 : \frac{31}{27}

Maximum (\frac{1}{3}, \frac{31}{27})

Plug

x = 1

into

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

Minimum (1, 1)

Maximum (\frac{1}{3}, \frac{31}{27}), Minimum (1, 1)

f (x) = 100 x (2 x + 3) (x - 5)

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

(x - 1) (x - 3)

f (x) = \frac{1}{6} x

y = x^{2} - 3 x - 10

What is the extreme f(x)=x^3-2x^2+x+1 ?
The extreme f(x)=x^3-2x^2+x+1 is Maximum(1/3 , 31/27),Minimum(1,1)