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

The extreme f(x)=1-x^3-3x-2x^2+3x^4 is Minimum(0.91397…,-2.08268…)

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

extreme points

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

Minimum (0.91397 \dots, - 2.08268 \dots)

Solution steps

Find the critical points:

x \approx 0.91397 \dots

Domain of

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

Find intervals:

Decreasing

: - \infty < x < 0.91397 \dots,

Increasing

: 0.91397 \dots < x < \infty

Plug the extreme point

x = 0.91397 \dots

into

1 - x^{3} - 3 x - 2 x^{2} + 3 x^{4} \Rightarrow y = - 2.08268 \dots

Minimum (0.91397 \dots, - 2.08268 \dots)

f (x) = (x - 1) (x + 2) (x + 4)

f (x) = 4 x^{5} - 3 x^{3} - 3 x + 1

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

w (x, y) = 6 + \frac{3 x y}{75}

f (x) = 14 x y - x^{3} - 7 y^{2}

What is the extreme f(x)=1-x^3-3x-2x^2+3x^4 ?
The extreme f(x)=1-x^3-3x-2x^2+3x^4 is Minimum(0.91397…,-2.08268…)