What is the average rate of change for this function for the interval fron x=2 to x=4

The average rate of change is 27.5.

The calculation is as follows:

When X = 2 so Y = 9

And,

When X = 4 So Y = 64

Now

The average rate of change is

= 27.5

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Subtract the two Y values of X = 2 and X = 4 to find the total difference, then divide by the difference between X=2 and X =4

When X = 2 Y = 9
When X = 4 Y = 64

Difference between the two Y values = 64 -9 = 55
Difference between the two X values = 4-2 = 2

The rate of change = difference in Y divided by difference in X:

55/2 = 27.5

If the diameter is 8 than the radius is 4 because 2r or 2*radius equals the diameter. 4*2=8. 8/2=4.