What is the inflection x^4-12x^2+x-1 ?

The inflection x^4-12x^2+x-1 is (-sqrt(2),-21-sqrt(2)),(sqrt(2),sqrt(2)-21)

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inflection x^4-12x^2+x-1

inflection points

x^{4} - 12 x^{2} + x - 1

(- 2, - 21 - 2), (2, 2 - 21)

Solution steps

f^{''} (x) = 12 x^{2} - 24

Find intervals:

Concave Upward

: - \infty < x < - 2,

Concave Downward

: - 2 < x < 2,

Concave Upward

: 2 < x < \infty

Plug

x = - 2

into

x^{4} - 12 x^{2} + x - 1 : - 21 - 2

(- 2, - 21 - 2)

Plug

x = 2

into

x^{4} - 12 x^{2} + x - 1 : 2 - 21

(2, 2 - 21)

(- 2, - 21 - 2), (2, 2 - 21)

What is the inflection x^4-12x^2+x-1 ?
The inflection x^4-12x^2+x-1 is (-sqrt(2),-21-sqrt(2)),(sqrt(2),sqrt(2)-21)