Question

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

Answer 1

Answer:

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

$\frac{f(b)-f(a)}{b-a}$

In this problem we have

$a=-5$

$b=0$

$f(a)=f(-5)=9$  

$f(b)=f(0)=0$

Substitute

$\frac{9-0}{0+5}=9/5$

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

$\frac{f(b)-f(a)}{b-a}$

In this problem we have

$a=-10$

$b=-2$

$f(a)=f(-10)=-5$  

$f(b)=f(-2)=-5$

Substitute

$\frac{-5+5}{-2+10}=0$

so

Interval C the rate of change is zero

therefore

Intervals A and C only

Answer 2

Answer:

Intervals A and C only