What is the extreme f(x)=6x^4+11x^3-x^2+x ?

The extreme f(x)=6x^4+11x^3-x^2+x is Minimum(-1.45214…,-10.56446…)

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extreme f(x)=6x^4+11x^3-x^2+x

extreme points

f (x) = 6 x^{4} + 11 x^{3} - x^{2} + x

Minimum (- 1.45214 \dots, - 10.56446 \dots)

Solution steps

Find the critical points:

x \approx - 1.45214 \dots

Domain of

6 x^{4} + 11 x^{3} - x^{2} + x : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < - 1.45214 \dots,

Increasing

: - 1.45214 \dots < x < \infty

Plug the extreme point

x = - 1.45214 \dots

into

6 x^{4} + 11 x^{3} - x^{2} + x \Rightarrow y = - 10.56446 \dots

Minimum (- 1.45214 \dots, - 10.56446 \dots)

f (x) = - 25 x^{2} - 20 y^{2} + 300 x + 480 y + 200

24 x^{3} - 3 x^{4} - x^{3} (24 - 3 x)

y = 9 x + 9 sin (x), 0 \leq x \leq 2 π

f (x) = 5 x^{2} - 10 x + 2

f (x) = 5 x^{2} - 10 x + 8

What is the extreme f(x)=6x^4+11x^3-x^2+x ?
The extreme f(x)=6x^4+11x^3-x^2+x is Minimum(-1.45214…,-10.56446…)