Answer
The film length that received highest rating is $10$ minutes.
Work Step by Step
The rating is given by, $R(t)=\frac{20t}{t^2+100}$, where $t$ is the film length in minutes.
To find critical points equate $R'(t)=0$.
$R'(t):=2000-20t^2=0\implies t=\pm10$
The film length cannot be negative, hence $t=10$.
To check if the rating is maximum at $t=10$, $R'(9)=380>0$ and $R'(11)=-420<0$. The sign changes from $+$ to $-$ about $t=10$, hence the rating is maximum at $t=10$ minutes.
