What is the extreme 3x^3-3x^2-3x+2 ?

The extreme 3x^3-3x^2-3x+2 is Maximum(-1/3 , 23/9),Minimum(1,-1)

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extreme 3x^3-3x^2-3x+2

extreme points

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

Maximum (- \frac{1}{3}, \frac{23}{9}), Minimum (1, - 1)

Solution steps

f^{'} (x) = 9 x^{2} - 6 x - 3

Find intervals:

Increasing

: - \infty < x < - \frac{1}{3},

Decreasing

: - \frac{1}{3} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - \frac{1}{3}

into

3 x^{3} - 3 x^{2} - 3 x + 2 : \frac{23}{9}

Maximum (- \frac{1}{3}, \frac{23}{9})

Plug

x = 1

into

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

Minimum (1, - 1)

Maximum (- \frac{1}{3}, \frac{23}{9}), Minimum (1, - 1)

f (x) = - x^{2} + 2 x + 5

f (x) = 3 x^{3} - x^{2} + 4 x - 2

f (x, y) = - 96 \cdot x + 2 \cdot x^{3} + 6 \cdot x \cdot y^{2} - 3 \cdot y^{3}

y = x^{3} - 3 x^{2} - 9 x + 5

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

What is the extreme 3x^3-3x^2-3x+2 ?
The extreme 3x^3-3x^2-3x+2 is Maximum(-1/3 , 23/9),Minimum(1,-1)