What is the extreme x^4+2x^3+x^2+x+1 ?

The extreme x^4+2x^3+x^2+x+1 is Minimum(-1.26068…,-0.15267…)

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extreme x^4+2x^3+x^2+x+1

extreme points

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

Minimum (- 1.26068 \dots, - 0.15267 \dots)

Solution steps

Find the critical points:

x \approx - 1.26068 \dots

Domain of

x^{4} + 2 x^{3} + x^{2} + x + 1 : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < - 1.26068 \dots,

Increasing

: - 1.26068 \dots < x < \infty

Plug the extreme point

x = - 1.26068 \dots

into

x^{4} + 2 x^{3} + x^{2} + x + 1 \Rightarrow y = - 0.15267 \dots

Minimum (- 1.26068 \dots, - 0.15267 \dots)

f (x) = x^{2} - 4 x y + y^{2} - 4

f (x) = 15 x^{2} - 60 x + 25

f (x) = 10 sin (2 x), (- 2 π, 2 π)

- \frac{1}{2} x^{4} + \frac{4}{3} x^{3} - 14

What is the extreme x^4+2x^3+x^2+x+1 ?
The extreme x^4+2x^3+x^2+x+1 is Minimum(-1.26068…,-0.15267…)