Question

F(x)=x^2 −x−1 Over which interval does f have an average rate of change of zero?

Answer 1

C. -1 < x < 2.

Explanation:

Change to vertex form to find the axis of symmetry:

x^2 − x −1

= (x - 0.5)^2 - 0.25 - 1

= (x - 0.5)^2 - 1.25.

Thus the graph is symmetrical about x = 0.5.

So the interval must be equal lengths either side of x = 0.5.

That would be -1 < x < 2.