F (x) = x^2-x-1

Over which interval does f have an average rate of change of zero?

Choose 1 answer:

(Choice A)

2≤x≤3

(Choice B)

-5≤x≤5

(Choice C)

2-1≤x≤2

(Choice D)

-3≤x≤-2

C. - 1 < x < 2.

Step-by-step 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.