on which interval does ( h(x) ) have an average rate of change of zero?\nchoose 1 answer!\n(a) ( -5 leq x…

on which interval does ( h(x) ) have an average rate of change of zero?\nchoose 1 answer!\n(a) ( -5 leq x leq 0 )\n(b) ( 5 leq x leq 7 )\n(c) ( -9 leq x leq -5 )\n(d) ( 0 leq x leq 5 )

on which interval does ( h(x) ) have an average rate of change of zero?\nchoose 1 answer!\n(a) ( -5 leq x leq 0 )\n(b) ( 5 leq x leq 7 )\n(c) ( -9 leq x leq -5 )\n(d) ( 0 leq x leq 5 )

Answer

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function (y = h(x)) over the interval ([a,b]) is given by (\frac{h(b)-h(a)}{b - a}). If the average rate of change is zero, then (h(b)=h(a)).

Step2: Analyze each interval

  • For interval (-5\leq x\leq0): Let (a=-5) and (b = 0). From the graph, (h(-5)\neq h(0)) ( (h(-5)) is approximately (2) and (h(0)=7)).
  • For interval (5\leq x\leq7): Let (a = 5) and (b=7). From the graph, (h(5)\neq h(7)) ( (h(5)=-3) and (h(7)) is between (3) and (4)).
  • For interval (-9\leq x\leq - 5): Let (a=-9) and (b=-5). From the graph, the function is constant over this interval. So, (h(-9)=h(-5)). Then (\frac{h(-5)-h(-9)}{-5-(-9)}=\frac{h(-5)-h(-5)}{4}=0).
  • For interval (0\leq x\leq5): Let (a = 0) and (b = 5). From the graph, (h(0)=7) and (h(5)=-3), so (h(0)\neq h(5)).

Answer:

C. (-9\leq x\leq - 5)