Question

group of researchers found that people prefer training films of moderate length; shorter films contain too little information, while longer films are boring. For a training film on the care of exotic birds, the researchers determined that the ratings people gave for the film could be approximated by, R(t)= t 2 +100 20t where t is the length of the film (in minutes). Find the film length that received the highest rating.

Answer 1

To find the film length that received the highest rating, determine the maximum value of the rating function R(t)= t^2 + 100 - 20t. The film length that received the highest rating is 10 minutes.

Step-by-step explanation:

To find the film length that received the highest rating, we need to determine the maximum value of the rating function R(t)= t^2 + 100 - 20t. One way to find the maximum value is by finding the critical points of the function, which occur when the derivative is equal to zero. So, let's find the derivative of R(t): R'(t) = 2t - 20. Setting this equal to zero, we have 2t - 20 = 0. Solving for t, we get t = 10. Since the second derivative is positive at t = 10, we can conclude that this critical point is a maximum. Therefore, the film length that received the highest rating is 10 minutes.