Instructions: drag each value to the correct location on the table. each value can be used more than once, but not all values will be used. the function f(x) = x3 + 4x2 + 2x + 1 is graphed above. match the intervals in the table with their respective average rates of change for this function.

Your dragged values will be (from left to right) ...

... 1 ... -1 ... -3 ... -1 ... 1

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When there is tedious calculation involved, I prefer to let a graphing calculator or spreadsheet do the work. (See attached)

Just to show you what is involved, here's the first one.

... f(-3) = 4 . . . . . you are supposed to read this from your graph. IMO, your graph is a little off.

... f(-2) = 5

Then the average rate of change on the interval [-3, -2] is

... (change in f(x)) / (change in x)

... (f(-2) - f(-3)) / (-2 - (-3)) = (5-4)/(1) = 1.