Question

Find the average rate of change for the following function on the indicated intervals: f(x)=x^3-2x; [0,4]

Answer 1

Average rate of change (as opposed to instantaneous, which is the derivative) is just the same thing as the slope of the line between the two points. For the first one, f(0) = 0, and f(4) = (4)^3 - 2(4) = 64 - 8 = 56

Slope = (y2 - y1)/(x2 - x1) = (56 - 0)/(4 - 0) = (56/4) = 14.