What is the extreme f(x)=x(x^3-x+10) ?

The extreme f(x)=x(x^3-x+10) is Minimum(-1.47970…,-12.19254…)

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extreme f(x)=x(x^3-x+10)

extreme points

f (x) = x (x^{3} - x + 10)

Minimum (- 1.47970 \dots, - 12.19254 \dots)

Solution steps

Find the critical points:

x \approx - 1.47970 \dots

Domain of

x (x^{3} - x + 10) : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < - 1.47970 \dots,

Increasing

: - 1.47970 \dots < x < \infty

Plug the extreme point

x = - 1.47970 \dots

into

x (x^{3} - x + 10) \Rightarrow y = - 12.19254 \dots

Minimum (- 1.47970 \dots, - 12.19254 \dots)

f (x) = - 462 x + 64 x^{2} - 2 x^{3}

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

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

f (x) = - 5 x^{7} ln (2 x), (0, 6)

- x^{3} + 12 x

What is the extreme f(x)=x(x^3-x+10) ?
The extreme f(x)=x(x^3-x+10) is Minimum(-1.47970…,-12.19254…)