13C - Average rate of change
When the relationship between two variables is variable (non-linear), we can find the average rate of change. The average rate of change is found by calculating the gradient of a line segment drawn between two points, \((x_1,y_1)\) and \((x_2,y_2)\), on a graph:
\[Av ROC=m=\frac{y_2-y_1}{x_2-x_1}\]
13C - Example 1: Average rate of change between two points
Consider the graph below which shows a planes height (meters) with respect to time (minutes) for half of the flight. What is the average rate of change between:
(a) \(t=0\) and \(t=10\). (b) \(t=10\) and \(t=90\). |
13C - Example 1: Video solution
13C - Example 1: Practice
Question 1: ABC Question 2: ABC 13C - Example 1: Solutions
Question 1: ABC Question 2: ABC |
Average rate of change of a function:
For any function, \(y=f(x)\), the average rate of change over an interval \(x\in[a,b]\) is given by the gradient of a line segment joining the point \((a,f(a))\) and \((b,f(b))\):
\[AvROC=\frac{f(b)-f(a)}{b-a}\]
For any function, \(y=f(x)\), the average rate of change over an interval \(x\in[a,b]\) is given by the gradient of a line segment joining the point \((a,f(a))\) and \((b,f(b))\):
\[AvROC=\frac{f(b)-f(a)}{b-a}\]
13C - Example 2: Average rate of change of a function
Find the average rate of change for the function \(f(x)=x^2-4\) between \(x=1\) and \(x=4\).
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13C - Example 2: Video solution
13C - Example 2: Practice
Question 1: ABC Question 2: ABC 13C - Example 2: Solutions
Question 1: ABC Question 2: ABC |
13C - Example 3: Average rate of change of a function
The temperature of a room can be modelled by the following function where \(T\) is the temperature (Degrees Celsius) and \(t\) is the time (hours) after 6:00am: \[T(t)=16+5sin(\frac{\pi t}{12})\]What is the average rate of change in the temperature between 6:00am and 8:00am?
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13C - Example 3: Video solution
13C - Example 3: Practice
Question 1: ABC Question 2: ABC 13C - Example 3: Solutions
Question 1: ABC Question 2: ABC |