# Question #7ec7d

Apr 8, 2017

#### Explanation:

$y = \frac{6 x}{{x}^{2} + 3}$

The domain is $\mathbb{R}$

$y ' = \frac{- 6 \left({x}^{2} - 3\right)}{{x}^{2} + 3}$

$y ' ' = \frac{12 x \left({x}^{2} - 9\right)}{{x}^{2} + 3} ^ 3$

$y ' ' = 0$ at $x = 0$, $3$ and $- 3$.

The denominator of $y ' '$ is always positive and the numerator changes sign at each of its three zeros.

Therefore, $y ' '$ changes sign 3 times.