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

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

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

concavity

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

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

f (c) = - 44 c

f (x) = 8 - x, (- 3, 5)

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

y = x

y = tan (\frac{x - π}{2})