Average Rates of Change By the end of today’s class, I will be able to:  calculate the Slope of a Secant for any polynomial function  understand that A.R.C. (Average Rate of Change) gives a rate that approximately describes the graph as “generally increasing” or “generally decreasing” for a specified interval

Average Rates of Change Given a function, y = f(x), the Average RoC (“Rate of Change”) of y with respect to x, over an interval from x1 to x2 is given by the Slope of the Secant through (x1, y1) and (x2, y2) << A secant is a line that has 2 points of intersection with the curve. >> A.R.C. = =

Average Rates of Change Given: (-2,14) A.R.C. = = (4,-4) Therefore between x=-2 and x=4, the y-coordinate is decreasing at an average rate of 3 units/unit!

Average Rates of Change For Non-Linear Functions: - R.o.C. varies depending on the location on the curve - A.R.C. = +ve implies 1) secant is rising right 2) generally an interval of increase (increasing y-values) - A.R.C. = -ve implies 1) secant is falling right 2) generally an interval of decrease (decreasing y-values)

Average Rates of Change For Linear Functions: - R.o.C. is constant - equals the slope of the linear function

Modeling Example #4 on p. 74 h(t) = -5t2 + 10t + 120, t ”belongs to the real interval of” (4, 5) A.R.C. = = “Therefore” between 4s & 5s, the height of the rock is decreasing at an average rate of 35m/s

Now try the following! Read: p.68-74 Do: p.76 #24,9,10,13,15