What is the extreme f(x)=x^4+8x^3+22x^2+24x+9 ?

The extreme f(x)=x^4+8x^3+22x^2+24x+9 is Minimum(-3,0),Maximum(-2,1),Minimum(-1,0)

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extreme f(x)=x^4+8x^3+22x^2+24x+9

extreme points

f (x) = x^{4} + 8 x^{3} + 22 x^{2} + 24 x + 9

Minimum (- 3, 0), Maximum (- 2, 1), Minimum (- 1, 0)

Solution steps

f^{'} (x) = 4 x^{3} + 24 x^{2} + 44 x + 24

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < - 2,

Decreasing

: - 2 < x < - 1,

Increasing

: - 1 < x < \infty

Plug

x = - 3

into

x^{4} + 8 x^{3} + 22 x^{2} + 24 x + 9 : 0

Minimum (- 3, 0)

Plug

x = - 2

into

x^{4} + 8 x^{3} + 22 x^{2} + 24 x + 9 : 1

Maximum (- 2, 1)

Plug

x = - 1

into

x^{4} + 8 x^{3} + 22 x^{2} + 24 x + 9 : 0

Minimum (- 1, 0)

Minimum (- 3, 0), Maximum (- 2, 1), Minimum (- 1, 0)

f (x, y) = 2 x^{3} + 6 x y^{2} - 3 y^{3} - 150 x

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

f (x) = 12 x + ln (x)

ln (27 + 8 x^{3})

x^{3} - 6 x^{2} - 15 x + 7

What is the extreme f(x)=x^4+8x^3+22x^2+24x+9 ?
The extreme f(x)=x^4+8x^3+22x^2+24x+9 is Minimum(-3,0),Maximum(-2,1),Minimum(-1,0)