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

The extreme f(x)=x^3-3x^2-3x-1 is Maximum(1-sqrt(2),4sqrt(2)-6),Minimum(1+sqrt(2),-6-4sqrt(2))

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

extreme points

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

Maximum (1 - 2, 42 - 6), Minimum (1 + 2, - 6 - 42)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2 + 1,

Decreasing

: - 2 + 1 < x < 2 + 1,

Increasing

: 2 + 1 < x < \infty

Plug

x = 1 - 2

into

x^{3} - 3 x^{2} - 3 x - 1 : 42 - 6

Maximum (1 - 2, 42 - 6)

Plug

x = 1 + 2

into

x^{3} - 3 x^{2} - 3 x - 1 : - 6 - 42

Minimum (1 + 2, - 6 - 42)

Maximum (1 - 2, 42 - 6), Minimum (1 + 2, - 6 - 42)

f (x) = 4 x^{2} - 8 x + 3

f (x, y) = x^{2} + x y + \frac{1}{2} y^{2} - 5 x + y

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

(x^{2} + 3 x - 1)^{\frac{1}{3}}

f (x, y) = 5 x^{2} + 5 y^{2} + 20 x - 10 y + 40

What is the extreme f(x)=x^3-3x^2-3x-1 ?
The extreme f(x)=x^3-3x^2-3x-1 is Maximum(1-sqrt(2),4sqrt(2)-6),Minimum(1+sqrt(2),-6-4sqrt(2))