What is the extreme x^2(x-5)(x^2+4x+8) ?

The extreme x^2(x-5)(x^2+4x+8) is Maximum(0,0),Minimum(3.80133…,-652.22642…)

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extreme x^2(x-5)(x^2+4x+8)

extreme

Maximum (0, 0), Minimum (3.80133 \dots, - 652.22642 \dots)

Solution steps

Find the critical points:

x = 0, x \approx 3.80133 \dots

Domain of

x^{2} (x - 5) (x^{2} + 4 x + 8) : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3.80133 \dots,

Increasing

: 3.80133 \dots < x < \infty

Plug the extreme point

x = 0

into

x^{2} (x - 5) (x^{2} + 4 x + 8) \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = 3.80133 \dots

into

x^{2} (x - 5) (x^{2} + 4 x + 8) \Rightarrow y = - 652.22642 \dots

Minimum (3.80133 \dots, - 652.22642 \dots)

Maximum (0, 0), Minimum (3.80133 \dots, - 652.22642 \dots)

What is the extreme x^2(x-5)(x^2+4x+8) ?
The extreme x^2(x-5)(x^2+4x+8) is Maximum(0,0),Minimum(3.80133…,-652.22642…)