Question

\\(t(d)\\) is a function that relates the number of tickets sold for a movie to the number of days since the movie was released. the average rate of change in \\(t(d)\\) for the interval \\(d = 4\\) and \\(d = 10\\) is 0. which statement must be true?

• the same number of tickets was sold on the fourth day and tenth day
• no tickets were sold on the fourth day and tenth day
• fewer tickets were sold on the fourth day than on the tenth day
• more tickets were sold on the fourth day than on the tenth day

Explanation:

Define average rate of change formula

$$ \text{Average Rate of Change} = \frac{T(10) - T(4)}{10 - 4} $$

Set average rate of change to zero and solve

$$
LATEXBLOCK0
$$

Answer:

• (A) The same number of tickets was sold on the fourth day and tenth day (Correct answer)
• (B) No tickets were sold on the fourth day and tenth day
• (C) Fewer tickets were sold on the fourth day than on the tenth day
• (D) More tickets were sold on the fourth day than on the tenth day