Question

F(x) = x2 - x - 1
What is the average rate of change of f over the interval -1 < x < 1?

Answer 1

-1

Explanation:

The average rate of change is the ratio of the difference in y-values to the difference in x-values of corresponding points.

At x=-1, f(x) = (-1)^2 -(-1) -1 = 1

At x=1, f(x) = (1)^2 -(1) -1 = -1

So, points on the graph are (-1, 1) and (1, -1).

Then the change in y over that interval is -1 -1 = -2.

The change in x over that interval is 1 -(-1) = 2.

The average rate of change is ...

∆y/∆x = -2/2 = -1 . . . . average rate of change on (-1, 1)