Question

G(x)=-x^2/4+7

Over which interval does have a negative average rate of change?

Answer 1

Answer:
`(-\infty, 0]`

Explanation:

This is a parabola that opens down (because of the negative leading coefficient).

So, the average rate of change (i.e., the slope of the secant) is negative when the function is decreasing.

The function is decreasing to the left of the vertex, which is at (0, 7).

So, the function has a negative average rate of change for
`(-\infty, 0]`.

• Note that although there is a stationary point at x = 0, and that the graph isn't decreasing at this point, the average rate of change is still negative when considering a point to the left.