What is the extreme f(x)=3x^4+8x^3-6x^2+24x ?

The extreme f(x)=3x^4+8x^3-6x^2+24x is Minimum(-2.65896…,-106.67008…)

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extreme f(x)=3x^4+8x^3-6x^2+24x

extreme

Minimum (- 2.65896 \dots, - 106.67008 \dots)

Solution steps

Find the critical points:

x \approx - 2.65896 \dots

Domain of

3 x^{4} + 8 x^{3} - 6 x^{2} + 24 x : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < - 2.65896 \dots,

Increasing

: - 2.65896 \dots < x < \infty

Plug the extreme point

x = - 2.65896 \dots

into

3 x^{4} + 8 x^{3} - 6 x^{2} + 24 x \Rightarrow y = - 106.67008 \dots

Minimum (- 2.65896 \dots, - 106.67008 \dots)

What is the extreme f(x)=3x^4+8x^3-6x^2+24x ?
The extreme f(x)=3x^4+8x^3-6x^2+24x is Minimum(-2.65896…,-106.67008…)