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

The extreme f(x)=x^3-3x^2-9x+2 is Maximum(-1,7),Minimum(3,-25)

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

extreme

Maximum (- 1, 7), Minimum (3, - 25)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 1

into

x^{3} - 3 x^{2} - 9 x + 2 : 7

Maximum (- 1, 7)

Plug

x = 3

into

x^{3} - 3 x^{2} - 9 x + 2 : - 25

Minimum (3, - 25)

Maximum (- 1, 7), Minimum (3, - 25)

What is the extreme f(x)=x^3-3x^2-9x+2 ?
The extreme f(x)=x^3-3x^2-9x+2 is Maximum(-1,7),Minimum(3,-25)