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

The extreme f(x)=3x^3-x^2+1 is Maximum(0,1),Minimum(2/9 , 239/243)

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

extreme points

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

Maximum (0, 1), Minimum (\frac{2}{9}, \frac{239}{243})

Solution steps

f^{'} (x) = 9 x^{2} - 2 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{2}{9},

Increasing

: \frac{2}{9} < x < \infty

Plug

x = 0

into

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

Maximum (0, 1)

Plug

x = \frac{2}{9}

into

3 x^{3} - x^{2} + 1 : \frac{239}{243}

Minimum (\frac{2}{9}, \frac{239}{243})

Maximum (0, 1), Minimum (\frac{2}{9}, \frac{239}{243})

x^{2} - x

f (x) = - x - 9

(4, 7), (1, 6)

- 5 x + 4

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

What is the extreme f(x)=3x^3-x^2+1 ?
The extreme f(x)=3x^3-x^2+1 is Maximum(0,1),Minimum(2/9 , 239/243)