What is the f(x)=(x^2(x+1))/((x^2+1)^{3/2)} ?

The f(x)=(x^2(x+1))/((x^2+1)^{3/2)} is

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f(x)=(x^2(x+1))/((x^2+1)^{3/2)}

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

Domain : - \infty < x < \infty

X Intercepts : (0, 0), (- 1, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Maximum - \frac{- 3 + 1 7 ^{\frac{1}{2}}}{2}, \frac{2 \cdot 2 ^{\frac{1}{2}} ( 29 - 7 \cdot 1 7 ^{\frac{1}{2}} )}{( 15 - 3 \cdot 1 7 ^{\frac{1}{2}} ) ^{\frac{3}{2}}}, Minimum (0, 0), Maximum \frac{3 + 1 7 ^{\frac{1}{2}}}{2}, \frac{2 \cdot 2 ^{\frac{1}{2}} ( 29 + 7 \cdot 1 7 ^{\frac{1}{2}} )}{( 15 + 3 \cdot 1 7 ^{\frac{1}{2}} ) ^{\frac{3}{2}}}

Interval Notation

Domain : (- \infty, \infty)

Solution steps

Domain of

\frac{x ^{2} ( x + 1 )}{( x ^{2} + 1 ) ^{\frac{3}{2}}} : - \infty < x < \infty

Axis interception points of

\frac{x ^{2} ( x + 1 )}{( x ^{2} + 1 ) ^{\frac{3}{2}}} :

X Intercepts

: (0, 0), (- 1, 0),

Y Intercepts

: (0, 0)

Asymptotes of

\frac{x ^{2} ( x + 1 )}{( x ^{2} + 1 ) ^{\frac{3}{2}}} :

None

Extreme Points of

\frac{x ^{2} ( x + 1 )}{( x ^{2} + 1 ) ^{\frac{3}{2}}} :

Maximum

- \frac{- 3 + 1 7 ^{\frac{1}{2}}}{2}, \frac{2 \cdot 2 ^{\frac{1}{2}} ( 29 - 7 \cdot 1 7 ^{\frac{1}{2}} )}{( 15 - 3 \cdot 1 7 ^{\frac{1}{2}} ) ^{\frac{3}{2}}},

Minimum

(0, 0),

Maximum

\frac{3 + 1 7 ^{\frac{1}{2}}}{2}, \frac{2 \cdot 2 ^{\frac{1}{2}} ( 29 + 7 \cdot 1 7 ^{\frac{1}{2}} )}{( 15 + 3 \cdot 1 7 ^{\frac{1}{2}} ) ^{\frac{3}{2}}}

What is the f(x)=(x^2(x+1))/((x^2+1)^{3/2)} ?
The f(x)=(x^2(x+1))/((x^2+1)^{3/2)} is