Summary

• The average rate of change of y = f (x) over an interval [x₀, x₁]:

• The instantaneous rate of change is the limit of the average rates of change.
• Graphical interpretation: Average rate of change is the slope of the secant line through the points (x₀, f (x₀)) and (x₁, f (x₁)) on the graph of f (x).
• Graphical interpretation: Instantaneous rate of change is the slope of the tangent line at x₀.
• To estimate the instantaneous rate of change at x = x₀, compute the average rate of change over several intervals [x₀, x₁] (or [x₁, x₀]) for x₁ close to x₀.
• The velocity of an object in linear motion is the rate of change of position s (t).
• Linear function f (x) = mx + b: The average rate of change over every interval and the instantaneous rate of change at every point are equal to the slope m.