What is the inflection f(x)=x^4-x^2+2 ?

The inflection f(x)=x^4-x^2+2 is (-1/(sqrt(6)), 67/36),(1/(sqrt(6)), 67/36)

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inflection f(x)=x^4-x^2+2

inflection points

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

(- \frac{1}{6}, \frac{67}{36}), (\frac{1}{6}, \frac{67}{36})

Solution steps

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

Find intervals:

Concave Upward

: - \infty < x < - \frac{1}{6},

Concave Downward

: - \frac{1}{6} < x < \frac{1}{6},

Concave Upward

: \frac{1}{6} < x < \infty

Plug

x = - \frac{1}{6}

into

x^{4} - x^{2} + 2 : \frac{67}{36}

(- \frac{1}{6}, \frac{67}{36})

Plug

x = \frac{1}{6}

into

x^{4} - x^{2} + 2 : \frac{67}{36}

(\frac{1}{6}, \frac{67}{36})

(- \frac{1}{6}, \frac{67}{36}), (\frac{1}{6}, \frac{67}{36})

f (x) = 4 x

f (x) = \frac{x ^{2} + 15 x + 54}{x + 6}

f (x) = - x + 6

y = \frac{5 x + 20}{x ^{2} - 16}

f (x) = (- \frac{1}{2} x^{2} + 5.5)

What is the inflection f(x)=x^4-x^2+2 ?
The inflection f(x)=x^4-x^2+2 is (-1/(sqrt(6)), 67/36),(1/(sqrt(6)), 67/36)