What is the extreme f(x)=x^3+3x^2-9x+1 ?

The extreme f(x)=x^3+3x^2-9x+1 is Maximum(-3,28),Minimum(1,-4)

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extreme f(x)=x^3+3x^2-9x+1

extreme

Maximum (- 3, 28), Minimum (1, - 4)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 3

into

x^{3} + 3 x^{2} - 9 x + 1 : 28

Maximum (- 3, 28)

Plug

x = 1

into

x^{3} + 3 x^{2} - 9 x + 1 : - 4

Minimum (1, - 4)

Maximum (- 3, 28), Minimum (1, - 4)

What is the extreme f(x)=x^3+3x^2-9x+1 ?
The extreme f(x)=x^3+3x^2-9x+1 is Maximum(-3,28),Minimum(1,-4)