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

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

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

extreme

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

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

Maximum (- 2, 42 + 1)

Plug

x = 2

into

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

Minimum (2, - 42 + 1)

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

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