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Popular Functions >

Find the Concavity f(x)=x/(x^2+1)

Solution

concavity

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

Solution

Concave Downward : - \infty < x < - 3, Concave Upward : - 3 < x < 0, Concave Downward : 0 < x < 3, Concave Upward : 3 < x < \infty

Solution steps

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

Find intervals:

Concave Downward

: - \infty < x < - 3,

Concave Upward

: - 3 < x < 0,

Concave Downward

: 0 < x < 3,

Concave Upward

: 3 < x < \infty

Concave Downward : - \infty < x < - 3, Concave Upward : - 3 < x < 0, Concave Downward : 0 < x < 3, Concave Upward : 3 < x < \infty

Graph

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Frequently Asked Questions (FAQ)

What is the concavity f(x)= x/((x^2+1)) ?
The concavity f(x)= x/((x^2+1)) is