What is the extreme 2x^3-2x^2-2x+9 ?

The extreme 2x^3-2x^2-2x+9 is Maximum(-1/3 , 253/27),Minimum(1,7)

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extreme 2x^3-2x^2-2x+9

extreme points

2 x^{3} - 2 x^{2} - 2 x + 9

Maximum (- \frac{1}{3}, \frac{253}{27}), Minimum (1, 7)

Solution steps

f^{'} (x) = 6 x^{2} - 4 x - 2

Find intervals:

Increasing

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

Decreasing

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

Increasing

: 1 < x < \infty

Plug

x = - \frac{1}{3}

into

2 x^{3} - 2 x^{2} - 2 x + 9 : \frac{253}{27}

Maximum (- \frac{1}{3}, \frac{253}{27})

Plug

x = 1

into

2 x^{3} - 2 x^{2} - 2 x + 9 : 7

Minimum (1, 7)

Maximum (- \frac{1}{3}, \frac{253}{27}), Minimum (1, 7)

f (x) = 320 x^{2} - 2560 x^{3}

f (x, y) = x^{2} - 4 x + y^{2} - 6 y - 2

f (x) = 4 x^{3} - x^{2} + 9

x^{2} - 6 x + 12

f (x) = \cdot f (y) - f (x, y) (x y) = 3 x + 3 y + 6

What is the extreme 2x^3-2x^2-2x+9 ?
The extreme 2x^3-2x^2-2x+9 is Maximum(-1/3 , 253/27),Minimum(1,7)