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

30

step-by-step explanation:

times by times

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."