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

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

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

extreme points

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

Minimum (- \frac{1}{2}, - 2 - 1), Maximum (\frac{1}{2}, 2 - 1)

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Decreasing

: \frac{1}{2} < x < \infty

Plug

x = - \frac{1}{2}

into

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

Minimum (- \frac{1}{2}, - 2 - 1)

Plug

x = \frac{1}{2}

into

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

Maximum (\frac{1}{2}, 2 - 1)

Minimum (- \frac{1}{2}, - 2 - 1), Maximum (\frac{1}{2}, 2 - 1)

2 cos (x) - sin (2 x)

(- 4, 1), (2, - 3)

\frac{1}{x} + 3

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

y = - 1

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