Question

Given the function f(x)= x’ – 2x + 7, what is its average rate of change over the interval 3?

(3) -5
(2) 12
(4) -7

Answer 1

The average rate of change of the given function over the interval from 3 to -5 is -23/8.

Step-by-step explanation:

The average rate of change of a function over an interval can be found by calculating the difference in the function values at the endpoints of the interval and dividing by the difference in the input values.

For the function f(x) = x' - 2x + 7, we need to find the average rate of change over the interval from 3 to -5. Evaluating the function at these points, we get f(3) = 3' - 2(3) + 7 = 4 and f(-5) = (-5)' - 2(-5) + 7 = 27.

So the average rate of change is (f(-5) - f(3))/(-5 - 3) = (27 - 4)/(-8) = -23/8.