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Popular >

inflection 1/(1+x^2)

Solution

inflection points

\frac{1}{1 + x ^{2}}

Solution

(- \frac{1}{3}, \frac{3}{4}), (\frac{1}{3}, \frac{3}{4})

Solution steps

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

Find intervals:

Concave Upward

: - \infty < x < - \frac{1}{3},

Concave Downward

: - \frac{1}{3} < x < \frac{1}{3},

Concave Upward

: \frac{1}{3} < x < \infty

Plug

x = - \frac{1}{3}

into

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

(- \frac{1}{3}, \frac{3}{4})

Plug

x = \frac{1}{3}

into

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

(\frac{1}{3}, \frac{3}{4})

(- \frac{1}{3}, \frac{3}{4}), (\frac{1}{3}, \frac{3}{4})

Popular Examples

asymptotes of f(x)=(3x-5)/(4x+13)asymptotes

f (x) = \frac{3 x - 5}{4 x + 13}

parity f(x)= 1/(6x^3)parity

f (x) = \frac{1}{6 x ^{3}}

domain of g(x)= 3/(x-4)domain

g (x) = \frac{3}{x - 4}

line (5,14),(2,8)line

(5, 14), (2, 8)

domain of-(x-6)^2+1 domain

- (x - 6)^{2} + 1

Frequently Asked Questions (FAQ)

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