Average Rate of Change The average rate of change of a function on a short interval [x, x + h] for a fixed value of h is a function itself. Sometimes it is a function that we can recognize by its graph.
a. Graph y1 = sin(x) on a graphing calculator and its average rate of change y2 = (y1(x + 0.1) — y1(x))/0.1 for − 2π ≤ x ≤ 2 π. What familiar function does y2 look like?
b. Repeat part (a) fory1 = cos(x),y1 = ex,y1 = ln(x), and y1 = x2.
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