What is the extreme f(x)=2x^3-x^2-4x-1 ?

The extreme f(x)=2x^3-x^2-4x-1 is Maximum(-2/3 , 17/27),Minimum(1,-4)

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extreme f(x)=2x^3-x^2-4x-1

extreme points

f (x) = 2 x^{3} - x^{2} - 4 x - 1

Maximum (- \frac{2}{3}, \frac{17}{27}), Minimum (1, - 4)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3},

Decreasing

: - \frac{2}{3} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - \frac{2}{3}

into

2 x^{3} - x^{2} - 4 x - 1 : \frac{17}{27}

Maximum (- \frac{2}{3}, \frac{17}{27})

Plug

x = 1

into

2 x^{3} - x^{2} - 4 x - 1 : - 4

Minimum (1, - 4)

Maximum (- \frac{2}{3}, \frac{17}{27}), Minimum (1, - 4)

x 1 - x^{2}

f (x) = 2 x^{4} - 16 x^{2} + 3

f (x) = \frac{2}{5} x^{5} - 7 x^{4} + 30 x^{3} - 27

f (x, y) = 6 x y - 2 x^{2} y - 3 x y^{2}

f (x, y) = \frac{1}{x y}

What is the extreme f(x)=2x^3-x^2-4x-1 ?
The extreme f(x)=2x^3-x^2-4x-1 is Maximum(-2/3 , 17/27),Minimum(1,-4)