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

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

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

extreme points

y = 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) = x (15 - 43 + 2 x) (\frac{43}{2} - x)

f (x) = x (- 1)^{5}

f (x) = \frac{1}{3} \cdot x^{3} - \frac{1}{2} x^{2} - 6 x + 5

\frac{e ^{2 \cdot x}}{6 + 5 \cdot e ^{2 \cdot x}}

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

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