What is the extreme f(x)=x^4+4x^3+4x^2 ?

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

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extreme f(x)=x^4+4x^3+4x^2

extreme points

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

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

Solution steps

f^{'} (x) = 4 x^{3} + 12 x^{2} + 8 x

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

x^{4} + 4 x^{3} + 4 x^{2} : 0

Minimum (- 2, 0)

Plug

x = - 1

into

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

Maximum (- 1, 1)

Plug

x = 0

into

x^{4} + 4 x^{3} + 4 x^{2} : 0

Minimum (0, 0)

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

f (x, y) = 100 + x^{2} - y^{2}

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

f (x) = - 2 x^{4} + 16 x^{3} - 26

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

f (x, y) = 1 - x + y

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