to the right, you will see the graph of a function. ignoring whether it is increasing or decreasing, between…

to the right, you will see the graph of a function. ignoring whether it is increasing or decreasing, between which two x - values does the function have the greatest average rate of change?\n$x = 0$ and $x = 5$\n$x = 1$ and $x = 5$\n$x = 2$ and $x = 4$\n$x = 2$ and $x = 6$\ndone

to the right, you will see the graph of a function. ignoring whether it is increasing or decreasing, between which two x - values does the function have the greatest average rate of change?\n$x = 0$ and $x = 5$\n$x = 1$ and $x = 5$\n$x = 2$ and $x = 4$\n$x = 2$ and $x = 6$\ndone

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}).

Step2: Analyze each option

  • Option (x = 0) and (x = 5): Let's assume (f(0)\approx0) and (f(5)\approx0). Then the average rate of change is (\frac{f(5)-f(0)}{5 - 0}=\frac{0 - 0}{5}=0).
  • Option (x = 1) and (x = 5): Assume (f(1)\approx9) and (f(5)\approx0). The average rate of change is (\frac{f(5)-f(1)}{5 - 1}=\frac{0 - 9}{4}=-\frac{9}{4}=- 2.25).
  • Option (x = 2) and (x = 4): Assume (f(2)\approx11) and (f(4)\approx11). The average rate of change is (\frac{f(4)-f(2)}{4 - 2}=\frac{11 - 11}{2}=0).
  • Option (x = 2) and (x = 6): Assume (f(2)\approx11) and (f(6)\approx0). The average rate of change is (\frac{f(6)-f(2)}{6 - 2}=\frac{0 - 11}{4}=-\frac{11}{4}=-2.75).

Since we are ignoring the sign (as the problem says "ignoring whether it is increasing or decreasing", we are interested in the magnitude), (\left|\frac{f(6)-f(2)}{6 - 2}\right|=\frac{11}{4} = 2.75), (\left|\frac{f(5)-f(1)}{5 - 1}\right|=\frac{9}{4}=2.25), (\left|\frac{f(5)-f(0)}{5 - 0}\right| = 0), (\left|\frac{f(4)-f(2)}{4 - 2}\right|=0)

Answer:

(x = 2) and (x = 6)