What is the inflection f(x)=-x^4+3x^2-4 ?

The inflection f(x)=-x^4+3x^2-4 is (-1/(sqrt(2)),-11/4),(1/(sqrt(2)),-11/4)

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inflection f(x)=-x^4+3x^2-4

inflection points

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

(- \frac{1}{2}, - \frac{11}{4}), (\frac{1}{2}, - \frac{11}{4})

Solution steps

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

Find intervals:

Concave Downward

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

Concave Upward

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

Concave Downward

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

Plug

x = - \frac{1}{2}

into

- x^{4} + 3 x^{2} - 4 : - \frac{11}{4}

(- \frac{1}{2}, - \frac{11}{4})

Plug

x = \frac{1}{2}

into

- x^{4} + 3 x^{2} - 4 : - \frac{11}{4}

(\frac{1}{2}, - \frac{11}{4})

(- \frac{1}{2}, - \frac{11}{4}), (\frac{1}{2}, - \frac{11}{4})

f (x) = \frac{1}{x - 1} - 3

8 - 7 x

f (x) = 3 x - 3

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

What is the inflection f(x)=-x^4+3x^2-4 ?
The inflection f(x)=-x^4+3x^2-4 is (-1/(sqrt(2)),-11/4),(1/(sqrt(2)),-11/4)