Question

Using complete sentences, explain how to find the average rate of change for f(x) from x = 4 to x = 7. My equation is f(x)= -3(x-9)^2+2

Answer 1

The rate of change of a continuous function f(x) is the measure
of the inclination of the line that connects two points in the
curve of f(x). The inclination can be found by taking teh tangent
of the angle that this line makes with the x-axis. So the inclination
m is defined as:
m = tan(theta) = (f(x1) - f(x0))/(x1 - x0)
Where (x1, y1) and (x0, y0) are points in the curve f(x) of which
you are calculating the average rate of change.