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The gradient of a straight line graph is calculated as:
for two points and on the graph.
We can now define the average gradient between two points even if they are defined by a function which is not a straight line, and as:
This is the same as [link] .
Fill in the table by calculating the average gradient over the indicated intervals for the function . Note that ( ; ) is the co-ordinates of the first point and ( ; ) is the co-ordinates of the second point. So for AB, ( ; ) is the co-ordinates of point A and ( ; ) is the co-ordinates of point B.
A-B | |||||
A-C | |||||
B-C |
What do you notice about the gradients over each interval?
The average gradient of a straight-line function is the same over any two intervals on the function.
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