Question

What is the average rate of change of g(t) = -(t-1)² over the interval -4 ≤ t ≤ 5?

Answer 1

The average rate of change of the function g(t) = -(t-1)² over the interval -4 ≤ t ≤ 5 is calculated to be -41/9.

Step-by-step explanation:

The average rate of change of a function over an interval is calculated by finding the difference in function values at the endpoints of the interval, and dividing by the length of the interval. In the case of the function g(t) = -(t-1)² over the interval -4 ≤ t ≤ 5, we compute the average rate of change as follows:

1. First, we find the function values at t = -4 and t = 5. This gives us g(-4) = -(-4-1)² = 25 and g(5) = -(5-1)² = -16.
2. Next, we find the difference in these values: g(5) - g(-4) = -16 - 25 = -41.
3. Then, we divide this difference by the length of the interval: 5 - (-4) = 9.
4. So, the average rate of change of g(t) over the interval is -41/9.