To find the average rate of change of a function between any two points on its graph, we calculate the slope of the line containing the two points.

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Presentation transcript:

To find the average rate of change of a function between any two points on its graph, we calculate the slope of the line containing the two points.

For the data on the following screen … (a) By hand, draw a scatter diagram. (b) Draw a line through the points (1988, 71.4) and (1989, 71.7). (c) Find the average rate of change of life expectancy from 1988 to 1989. (d) Interpret the average rate of change found in (c).

(c) = 0.3 years per year (d) The average rate of change in life expectancy from 1988 to 1989 is 0.3 years.

y = f(x) Secant Line (x, f(x)) f(x) - f(c) (c, f(c)) x - c

Theorem Slope of a Secant Line The average rate of change of a function equals the slope of a secant line containing two points on its graph.

Determine where the following graph is increasing, decreasing and constant.

y 4 (2, 3) (4, 0) (1, 0) x (10, -3) (0, -3) (7, -3) -4

Increasing: (0, 2) Decreasing: (2, 7) Constant: (7, 10)