What is the extreme f(x)=x^4+2x^3+1x^2+1x+1 ?

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

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extreme f(x)=x^4+2x^3+1x^2+1x+1

extreme points

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

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

y = x^{2} - 3 x

y = 9 - 6 x^{2}, - 2 \leq x \leq 3

f (x) = 2 x^{3} + 4 x^{2} - 1

49 x + \frac{1}{x}

f (x) = - 0.1 x^{2} + 1.2 x + 5

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