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

The extreme f(x)=x^3-2x^2+x is Maximum(1/3 , 4/27),Minimum(1,0)

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

extreme points

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

Maximum (\frac{1}{3}, \frac{4}{27}), Minimum (1, 0)

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 : \frac{4}{27}

Maximum (\frac{1}{3}, \frac{4}{27})

Plug

x = 1

into

x^{3} - 2 x^{2} + x : 0

Minimum (1, 0)

Maximum (\frac{1}{3}, \frac{4}{27}), Minimum (1, 0)

y = x^{2} - x

f (x) = e^{x^{2}}

3 (\frac{1}{2})^{x}

\frac{3 x ^{2} - 12 x}{x ^{2} - 2 x - 3}

\frac{x ^{2} - 3}{x - 2}

What is the extreme f(x)=x^3-2x^2+x ?
The extreme f(x)=x^3-2x^2+x is Maximum(1/3 , 4/27),Minimum(1,0)