Find the average rate of change of f(x)=-x^2+2x+3 from x=2 to x=7

The rate of change between these on average is 11.

Step-by-step explanation:

In order to find these, we need to evaluate the equation at both points.

x^2 + 2x + 3

2^2 + 2(2) + 3

4 + 4 + 3

11

This gives us the ordered pair of (2, 11)

x^2 + 2x + 3

7^2 + 2(7) + 3

49 + 14 + 3

66

This gives us the ordered pair of (7, 66)

Now we use these two points in the slope formula to find the rate of change.

m(slope) = (y2 - y1)/(x2 - x1)

m = (66 - 11)/(7 - 2)

m = 55/5

m = 11