Question

Given the function h(x) =−x ^2 + 3x+ 10, determine the average rate of change of the function over the interval 0 ≤ x ≤ 4.

Answer 1

-1

Explanation:

To find the average rate of change of the function h(x) over the interval 0 ≤ x ≤ 4, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the difference in the x-values.

Let's evaluate h(x) at the endpoints:

For x = 0:

h(0) = -(0^2) + 3(0) + 10 = 10

For x = 4:

h(4) = -(4^2) + 3(4) + 10 = -16 + 12 + 10 = 6

The difference in the function values is h(4) - h(0) = 6 - 10 = -4.

The difference in the x-values is 4 - 0 = 4.

Now, we can calculate the average rate of change:

Average rate of change = (h(4) - h(0)) / (4 - 0) = -4 / 4 = -1.

Therefore, the average rate of change of the function h(x) over the interval 0 ≤ x ≤ 4 is -1.