Find the average rate of change of the function f ( x ) = − 2 x 2 + 3 x − 6 , from x=0 to x=4. note, the directions are equivalent to "find the average rate of change over the interval [0,4]". average rate of change =

The average rate of change has a relationship with slopes. Recall that we can write the slope of a line as follows:

We have the following function:

To find the Average Rate of Change (ARC), we need to compute the following:

So:

Finally, the Average Rate of Change is:

c. (3,2,6) is the answer.

if x = 1, then the answer is 3.5