Answer:
In the interval of - 2 ≤ t ≤ 4, the average rate of change is zero.
Step-by-step explanation:
The function is given to be [tex]g(t) = - (t - 1)^{2} + 5[/tex] ............ (1)
(i) Now, for 1 ≤ t ≤ 4, we will put t = 1 and t = 4.
So, g(1) = 5, g(4) = - 4. {From equation (1)}
Hence, g(1) ≠ g(4)
(ii) Now, for - 4 ≤ t ≤ - 3, we will put t = - 4 and t = - 3.
So, g(- 4) = - 20, g(- 3) = - 11. {From equation (1)}
Hence, g(- 4) ≠ g(- 3)
(iii) Now, for -2 ≤ t ≤ 0, we will put t = - 2 and t = 0.
So, g(- 2) = - 4, g(0) = 4. {From equation (1)}
Hence, g(- 2) ≠ g(0)
(iv) Now, for - 2 ≤ t ≤ 4, we will put t = - 2 and t = 4.
So, g(- 2) = - 4, g(4) = - 4. {From equation (1)}
Hence, g(- 2) = g(4)
Therefore, in the interval of - 2 ≤ t ≤ 4, the average rate of change is zero. (Answer)
