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
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
In this problem we have
[tex]a=-5[/tex]
[tex]b=0[/tex]
[tex]f(a)=f(-5)=9[/tex]
[tex]f(b)=f(0)=0[/tex]
Substitute
[tex]\frac{9-0}{0+5}=9/5[/tex]
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
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
In this problem we have
[tex]a=-10[/tex]
[tex]b=-2[/tex]
[tex]f(a)=f(-10)=-5[/tex]
[tex]f(b)=f(-2)=-5[/tex]
Substitute
[tex]\frac{-5+5}{-2+10}=0[/tex]
so
Interval C the rate of change is zero
therefore
Intervals A and C only
