Rate of Change (Unit 2 MCV4U)

In Calculus rate of change is one of the most critical concepts used for Calculus.

Consider this graph, we can tell that the graph is an example of a linear graph and that the rate of change is constant, but how do we calculate the rate of change of this graph? We use the formula

This is the formula in which you find the slop of a constant rate of change. You pinpoint two points on the graph and select one to be your y2 and x2 and subract them from y1 and x1. However there will be situations when there won't be a constant rate of change, an example of this is the function y = x^2

As we can see from the graph that the rate of change is changing, but that doesn't mean we can't pinpoint the rate of change at a certain point of the graph. Which is exactly a secent line is for,

as we can see the secant line crosses two points on the line and the two points that it crosses we use them to find the rate of change between those two points. For example lets say that a secant line on y = x^2 crosses between (1,1) and (2,4) we then use the slope of the secant line formula to find the rate of change. When we plug in the numbers the answer we get is 3, so the rate of change between the points (1,1) and (2,4) is 3.

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