average rate of change
The average rate of change is a mathematical concept that measures the overall change in a function over an interval
The average rate of change is a mathematical concept that measures the overall change in a function over an interval. It is a way to quantify how much a function is changing on average between two points.
To find the average rate of change, you need to calculate the slope of the secant line that connects the two points on the graph of the function. The formula for average rate of change is:
Average Rate of Change = (f(b) – f(a)) / (b – a)
Here, f(b) represents the value of the function at the ending point of the interval (b), and f(a) represents the value of the function at the starting point of the interval (a).
For example, let’s say we have the function f(x) = 2x + 3 and we want to find the average rate of change between x = 2 and x = 4:
f(4) = 2(4) + 3 = 11
f(2) = 2(2) + 3 = 7
Average Rate of Change = (11 – 7) / (4 – 2) = 4 / 2 = 2
Therefore, the average rate of change of the function f(x) = 2x + 3 between x = 2 and x = 4 is 2. This means that, on average, the function is increasing by 2 units for every 1 unit increase in x within the interval.
The average rate of change can also be interpreted as the slope of a straight line that connects the two points on the graph of the function. In our example, the line connecting the points (2, 7) and (4, 11) has a slope of 2, which matches the average rate of change we calculated.
Overall, the average rate of change is a useful concept in mathematics to measure and analyze the change in a function over a given interval.
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