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

The extreme f(x)=x^4+2x^3-2x^2+2x+1 is Minimum(-2.09219…,-11.09461…)

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

extreme points

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

Minimum (- 2.09219 \dots, - 11.09461 \dots)

Solution steps

Find the critical points:

x \approx - 2.09219 \dots

Domain of

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

Find intervals:

Decreasing

: - \infty < x < - 2.09219 \dots,

Increasing

: - 2.09219 \dots < x < \infty

Plug the extreme point

x = - 2.09219 \dots

into

x^{4} + 2 x^{3} - 2 x^{2} + 2 x + 1 \Rightarrow y = - 11.09461 \dots

Minimum (- 2.09219 \dots, - 11.09461 \dots)

\frac{1}{2 π} e^{- (x - 3)^{\frac{2}{2}}}

f (x) = 4 (e^{- 0.05 x} - e^{- 0.55 x})

f (x) = - x^{3} + 1.5 x^{2} + 36 x + 2

f (x, y) = 2 x^{2} + y^{2} - 4 x + 6 y

y = x e^{- 2 x}

What is the extreme f(x)=x^4+2x^3-2x^2+2x+1 ?
The extreme f(x)=x^4+2x^3-2x^2+2x+1 is Minimum(-2.09219…,-11.09461…)