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

The extreme x^4+2x^3+2x+2 is Minimum(-1.67765…,-2.87735…)

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

extreme points

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

Minimum (- 1.67765 \dots, - 2.87735 \dots)

Solution steps

Find the critical points:

x \approx - 1.67765 \dots

Domain of

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

Find intervals:

Decreasing

: - \infty < x < - 1.67765 \dots,

Increasing

: - 1.67765 \dots < x < \infty

Plug the extreme point

x = - 1.67765 \dots

into

x^{4} + 2 x^{3} + 2 x + 2 \Rightarrow y = - 2.87735 \dots

Minimum (- 1.67765 \dots, - 2.87735 \dots)

f (x, y) = x^{2} - y^{2} - 14 x + 2 y + 14

f (x, y) = (2 x + 3 y) (5 x + 7 y)

- 2 x^{4} + x^{3} + 6 x^{2} + x - 2

y = x^{4} - 5 x^{2} = x^{2} (x^{2} - 5)

f (x) = \frac{1}{x}, - 1 \leq x \leq 1

What is the extreme x^4+2x^3+2x+2 ?
The extreme x^4+2x^3+2x+2 is Minimum(-1.67765…,-2.87735…)