identifying decreasing average rates of change\nchoose the intervals where the graph has a\ndecreasing…

identifying decreasing average rates of change\nchoose the intervals where the graph has a\ndecreasing average rate of change\n( x = 0 ) to ( x = 1.3 )\n( x = 3 ) to ( x = 6 )\n( x = 4 ) to ( x = 6 )\n( x = 8 ) to ( x = 10 )

identifying decreasing average rates of change\nchoose the intervals where the graph has a\ndecreasing average rate of change\n( x = 0 ) to ( x = 1.3 )\n( x = 3 ) to ( x = 6 )\n( x = 4 ) to ( x = 6 )\n( x = 8 ) to ( x = 10 )

Answer

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function (y = f(x)) over the interval ([a,b]) is given by (\frac{f(b)-f(a)}{b - a}). A decreasing average rate of change means (\frac{f(b)-f(a)}{b - a}<0), or (f(b)<f(a)) (since (b>a) for an interval ([a,b])).

Step2: Analyze each interval

  • Interval (x = 0) to (x=13): Let (a = 0), (b = 13). From the graph, (f(0)=0) and (f(13)>0). Then (\frac{f(13)-f(0)}{13 - 0}=\frac{f(13)}{13}>0).
  • Interval (x = 3) to (x = 6): Let (a = 3), (b = 6). From the graph, (f(3)>f(6)). Then (\frac{f(6)-f(3)}{6 - 3}=\frac{\text{(negative value)}}{3}<0).
  • Interval (x = 4) to (x = 8): Let (a = 4), (b = 8). From the graph, (f(4)>f(8)). Then (\frac{f(8)-f(4)}{8 - 4}=\frac{\text{(negative value)}}{4}<0).
  • Interval (x = 8) to (x = 10): Let (a = 8), (b = 10). From the graph, (f(8)<f(10)). Then (\frac{f(10)-f(8)}{10 - 8}=\frac{\text{(positive value)}}{2}>0).

Answer:

(x = 3) to (x = 6), (x = 4) to (x = 8)