An automated solar tracker follows a path defined by the function

$$H(\varphi )={\varphi }^4+12{\varphi }^2+24\cos \varphi$$

for $-\pi \le \varphi \le \pi$, where $H$ is the vertical displacement in decimeters and $\varphi$ is the angle of rotation in radians. Determine whether the curve with equation $y=H(\varphi )$ has a point of inflection at the point where $\varphi =0$. Fully justify your answer.