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

The extreme x^4+2x^3+x^2+2x+2 is Minimum(-1.39816…,-0.48641…)

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

extreme points

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

Minimum (- 1.39816 \dots, - 0.48641 \dots)

Solution steps

Find the critical points:

x \approx - 1.39816 \dots

Domain of

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

Find intervals:

Decreasing

: - \infty < x < - 1.39816 \dots,

Increasing

: - 1.39816 \dots < x < \infty

Plug the extreme point

x = - 1.39816 \dots

into

x^{4} + 2 x^{3} + x^{2} + 2 x + 2 \Rightarrow y = - 0.48641 \dots

Minimum (- 1.39816 \dots, - 0.48641 \dots)

y = 3 x + 2 cos (x)

f (x, y) = x^{3} + y^{2} - 6 x y - 9 x + 8 y + 2

y = sin (x) + cos (x)

f (x) = 4 x^{2} + 40, - 1 \leq x \leq 1

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

What is the extreme x^4+2x^3+x^2+2x+2 ?
The extreme x^4+2x^3+x^2+2x+2 is Minimum(-1.39816…,-0.48641…)