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in this video weamp;#39;re going to focus on finding the average rate of change and the instantaneous rate of change so letamp;#39;s say if we have the function f ofx is equal to X raised to the 3 power how can we calculate the average rate of change on the interval from 1 to three now what we need to realize is that the average rate of change represents the slope of the secet line so hereamp;#39;s the graph x Cub or Y is equal to X Cube Y is the same as F ofx so at the point one and three which is these two points the slope of the secant line is the average rate of change the instantaneous rate of change is the SL of the Tang line so letamp;#39;s say if we wanted to find the instantaneous rate of change at xals 2 it would represent the slope of the tangent line the tangent line is a line that touches the curve at one point a secant line touches the curve at two points notice that you can approximate the slope of the the tangent line by finding the slope of the secant line if you w
