What is the extreme f(x)=-2x^3+6x-1 ?

The extreme f(x)=-2x^3+6x-1 is Minimum(-1,-5),Maximum(1,3)

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extreme f(x)=-2x^3+6x-1

extreme

Minimum (- 1, - 5), Maximum (1, 3)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

- 2 x^{3} + 6 x - 1 : - 5

Minimum (- 1, - 5)

Plug

x = 1

into

- 2 x^{3} + 6 x - 1 : 3

Maximum (1, 3)

Minimum (- 1, - 5), Maximum (1, 3)

What is the extreme f(x)=-2x^3+6x-1 ?
The extreme f(x)=-2x^3+6x-1 is Minimum(-1,-5),Maximum(1,3)