Question

given the funtions h(x) = x² + 3x - 5 determine the average rate of change pf the function over the interval -7 is less than or equal to x which is less than or equal to 1

Answer 1

The average rate of change of the function h(x) = x² + 3x - 5 over the interval -7 ≤ x ≤ 1 is -3.

Step-by-step explanation:

To determine the average rate of change of the function h(x) = x² + 3x - 5 over the interval -7 ≤ x ≤ 1, we need to find the difference in the values of the function at the endpoints of the interval and divide it by the difference in the x-values.

h(-7) = (-7)² + 3(-7) - 5 = 49 - 21 - 5 = 23
h(1) = (1)² + 3(1) - 5 = 1 + 3 - 5 = -1

The difference in the values is -1 - 23 = -24, and the difference in the x-values is 1 - (-7) = 8.

Therefore, the average rate of change is -24/8 = -3.