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in this video were going to focus on finding the average rate of change and the instantaneous rate of change so lets say if we have the function f of x is equal to x raised to the third power how can we calculate the average rate of change on the interval from one to three now we need to realize is that the average rate of change represents the slope of the secant line so heres the graph x cubed or y is equal to x cubed y is the same as f of x so at the point 1 and 3 which is these two points the slope of the secant line is the average rate of change the instantaneous rate of change is the slope of the tangent line so lets say if we wanted to find the instantaneous rate of change at x equals two 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 tangent line by finding the slope of the secant line if you want to find the slope o