What is the extreme f(x)= 1/4 x^4-x^3-4x+2 ?

The extreme f(x)= 1/4 x^4-x^3-4x+2 is Minimum(3.35530…,-17.50943…)

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extreme f(x)= 1/4 x^4-x^3-4x+2

extreme points

f (x) = \frac{1}{4} x^{4} - x^{3} - 4 x + 2

Minimum (3.35530 \dots, - 17.50943 \dots)

Solution steps

Find the critical points:

x \approx 3.35530 \dots

Domain of

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

Find intervals:

Decreasing

: - \infty < x < 3.35530 \dots,

Increasing

: 3.35530 \dots < x < \infty

Plug the extreme point

x = 3.35530 \dots

into

\frac{1}{4} x^{4} - x^{3} - 4 x + 2 \Rightarrow y = - 17.50943 \dots

Minimum (3.35530 \dots, - 17.50943 \dots)

What is the extreme f(x)= 1/4 x^4-x^3-4x+2 ?
The extreme f(x)= 1/4 x^4-x^3-4x+2 is Minimum(3.35530…,-17.50943…)