What is the extreme-x^4-x^3+x^2+3x+2 ?

The extreme-x^4-x^3+x^2+3x+2 is Maximum(0.85641…,4.13661…)

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extreme-x^4-x^3+x^2+3x+2

extreme points

- x^{4} - x^{3} + x^{2} + 3 x + 2

Maximum (0.85641 \dots, 4.13661 \dots)

Solution steps

Find the critical points:

x \approx 0.85641 \dots

Domain of

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

Find intervals:

Increasing

: - \infty < x < 0.85641 \dots,

Decreasing

: 0.85641 \dots < x < \infty

Plug the extreme point

x = 0.85641 \dots

into

- x^{4} - x^{3} + x^{2} + 3 x + 2 \Rightarrow y = 4.13661 \dots

Maximum (0.85641 \dots, 4.13661 \dots)

What is the extreme-x^4-x^3+x^2+3x+2 ?
The extreme-x^4-x^3+x^2+3x+2 is Maximum(0.85641…,4.13661…)