What is the extreme f(x)=x^4+6x^3-5x^2+2x+3 ?

The extreme f(x)=x^4+6x^3-5x^2+2x+3 is Minimum(-5.01805…,-257.01809…)

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extreme f(x)=x^4+6x^3-5x^2+2x+3

extreme points

f (x) = x^{4} + 6 x^{3} - 5 x^{2} + 2 x + 3

Minimum (- 5.01805 \dots, - 257.01809 \dots)

Solution steps

Find the critical points:

x = - 5.01805 \dots

Domain of

x^{4} + 6 x^{3} - 5 x^{2} + 2 x + 3 : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < - 5.01805 \dots,

Increasing

: - 5.01805 \dots < x < \infty

Plug the extreme point

x = - 5.01805 \dots

into

x^{4} + 6 x^{3} - 5 x^{2} + 2 x + 3 \Rightarrow y = - 257.01809 \dots

Minimum (- 5.01805 \dots, - 257.01809 \dots)

f (x) = x^{2} - 8 x + 17

f (x) = 8 x^{2} - x^{4}

f (t) = r (t) e^{- a t}

f (x) = 3 x^{4} + 4 x^{3} - 120 x^{2} + 120

What is the extreme f(x)=x^4+6x^3-5x^2+2x+3 ?
The extreme f(x)=x^4+6x^3-5x^2+2x+3 is Minimum(-5.01805…,-257.01809…)