What is the extreme x^4+3x^3+2x^2+x+1 ?

The extreme x^4+3x^3+2x^2+x+1 is Minimum(-1.76328…,-1.32505…)

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extreme x^4+3x^3+2x^2+x+1

extreme points

x^{4} + 3 x^{3} + 2 x^{2} + x + 1

Minimum (- 1.76328 \dots, - 1.32505 \dots)

Solution steps

Find the critical points:

x \approx - 1.76328 \dots

Domain of

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

Find intervals:

Decreasing

: - \infty < x < - 1.76328 \dots,

Increasing

: - 1.76328 \dots < x < \infty

Plug the extreme point

x = - 1.76328 \dots

into

x^{4} + 3 x^{3} + 2 x^{2} + x + 1 \Rightarrow y = - 1.32505 \dots

Minimum (- 1.76328 \dots, - 1.32505 \dots)

f (x) = - 0.4 x^{2} + 90 x - 2000, 0 \leq x

2 x^{2} - 2 x

f (x) = (x - 2)^{\frac{1}{8}}

y = 2 cos (x) - 11 x + 7 [- π, 0]

y = (x^{2} - 4)^{4} (x^{2} + 1)^{5}

What is the extreme x^4+3x^3+2x^2+x+1 ?
The extreme x^4+3x^3+2x^2+x+1 is Minimum(-1.76328…,-1.32505…)