Given the function f(x)=-x^2-5x+12f(x)=−x 2 −5x+12, determine the average rate of change of the function over the interval -5\le x \le 4−5≤x≤4.

Given:

The function is

To find:

The average rate of change of the function over the interval −5 ≤ x ≤ 4.

Solution:

The average rate of change of a function f(x) over the interval [a,b] is

Putting x=-5 in the given function, we get

Putting x=4 in the given function, we get

Now, the average rate of change of the function over the interval −5 ≤ x ≤ 4 is

Therefore, the average rate of change of the function over the interval −5 ≤ x ≤ 4 is -4.