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

The extreme f(x)=-x^3+3x-6 is Minimum(-1,-8),Maximum(1,-4)

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

extreme points

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

Minimum (- 1, - 8), Maximum (1, - 4)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

- x^{3} + 3 x - 6 : - 8

Minimum (- 1, - 8)

Plug

x = 1

into

- x^{3} + 3 x - 6 : - 4

Maximum (1, - 4)

Minimum (- 1, - 8), Maximum (1, - 4)

p er i o d i c i t y f (x) = 5 sin (\frac{1}{4} π x - π) - 3

am pl i t u d e 3 cos (π x - 2) + 5

in f l ec t i o n f (x) = x^{2} + 7 x + 1

s hi f t f (x) = 8 cos (2 x - 3 0^{\circ}) + 7

l in e m = 5, (2, 6)

What is the extreme f(x)=-x^3+3x-6 ?
The extreme f(x)=-x^3+3x-6 is Minimum(-1,-8),Maximum(1,-4)