What is the inflection x^4-3x^2 ?

The inflection x^4-3x^2 is (-1/(sqrt(2)),-5/4),(1/(sqrt(2)),-5/4)

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inflection x^4-3x^2

inflection points

x^{4} - 3 x^{2}

(- \frac{1}{2}, - \frac{5}{4}), (\frac{1}{2}, - \frac{5}{4})

Solution steps

f^{''} (x) = 12 x^{2} - 6

Find intervals:

Concave Upward

: - \infty < x < - \frac{1}{2},

Concave Downward

: - \frac{1}{2} < x < \frac{1}{2},

Concave Upward

: \frac{1}{2} < x < \infty

Plug

x = - \frac{1}{2}

into

x^{4} - 3 x^{2} : - \frac{5}{4}

(- \frac{1}{2}, - \frac{5}{4})

Plug

x = \frac{1}{2}

into

x^{4} - 3 x^{2} : - \frac{5}{4}

(\frac{1}{2}, - \frac{5}{4})

(- \frac{1}{2}, - \frac{5}{4}), (\frac{1}{2}, - \frac{5}{4})

f (x) = \frac{x - 4}{x}

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

y = - 3 x^{2} - 2 x + 5

(1, - 4), (- 2, 5)

\frac{x + 5}{x ^{2} + x - 6}

What is the inflection x^4-3x^2 ?
The inflection x^4-3x^2 is (-1/(sqrt(2)),-5/4),(1/(sqrt(2)),-5/4)