What is the extreme f(x)=x^3-6x^2+9x-3 ?

The extreme f(x)=x^3-6x^2+9x-3 is Maximum(1,1),Minimum(3,-3)

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extreme f(x)=x^3-6x^2+9x-3

extreme points

f (x) = x^{3} - 6 x^{2} + 9 x - 3

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

Solution steps

f^{'} (x) = 3 x^{2} - 12 x + 9

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 1

into

x^{3} - 6 x^{2} + 9 x - 3 : 1

Maximum (1, 1)

Plug

x = 3

into

x^{3} - 6 x^{2} + 9 x - 3 : - 3

Minimum (3, - 3)

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

What is the extreme f(x)=x^3-6x^2+9x-3 ?
The extreme f(x)=x^3-6x^2+9x-3 is Maximum(1,1),Minimum(3,-3)