Mean Value Theorem

The Mean Value Theorem states that if you have a smooth curve connecting two points on a graph, there’s at least one point on that curve where the slope of the tangent (the steepness) matches the average slope between the two endpoints. In simpler terms, if a car drives from one city to another, there’s a moment during the trip where its speed equals the average speed for the entire journey. This theorem highlights that instantaneous rates of change (like speed at a moment) relate closely to overall change over an interval.