For which intervals below is the average rate of change less than or equal to zero?

Interval
A -13 ≤ x ≤ -10
B -5 ≤ x ≤ 0
C -10 ≤ x ≤ -2
Intervals A and B only
Interval B and C only
Intervals A and C only
Intervals A, B and, C

Intervals A and C only

Step-by-step explanation:

we know that

The graph show a vertical parabola open upward

The vertex represent a minimum

The vertex is the point  (-6,-9)

Remember that the vertex is a turning point

That means

In the interval (-∞,-6) the function is decreasing (rate of change is negative)

In the interval (-6,∞) the function is increasing (rate of change is positive)

therefore

Verify each case

Interval A) A -13 ≤ x ≤ -10

Belong to the decreasing interval, so the rate of change is negative

Interval B) -5 ≤ x ≤ 0

Find the rate of change

the average rate of change is equal to

In this problem we have

Substitute

so

Interval B the rate of change is positive

Interval C) --10 ≤ x ≤ -2

Find the rate of change

the average rate of change is equal to

In this problem we have

Substitute

so

Interval C the rate of change is zero

therefore

Intervals A and C only