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

The extreme f(x)=x^3+6x^2+9x-3 is Maximum(-3,-3),Minimum(-1,-7)

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < - 1,

Increasing

: - 1 < x < \infty

Plug

x = - 3

into

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

Maximum (- 3, - 3)

Plug

x = - 1

into

x^{3} + 6 x^{2} + 9 x - 3 : - 7

Minimum (- 1, - 7)

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

f (x) = - 2 x^{3} + 6 x^{2} - 5

x^{4} - 8 x^{3} + 16 x^{2}

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

f (x, y) = 2 x^{2} - 8 x + y^{2} - 8 y + 6

f (x) = x e^{- 4 x}, 0 \leq x \leq 2

What is the extreme f(x)=x^3+6x^2+9x-3 ?
The extreme f(x)=x^3+6x^2+9x-3 is Maximum(-3,-3),Minimum(-1,-7)