Graphs 8
3 marks · EasyThe table shows part of the data for the function .
| x | y |
|---|---|
| 0 | 0 |
| 1 | 2 |
| 2 | 6 |
| 3 | 12 |
Estimate the gradient of the curve at using the values given.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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The estimated gradient at x=2 is 6 (±0.5)
Also accept: Working using difference quotients, e.g. (12-6)/(3-2)=6
Common mistakes: Uses (6-2)/(2-1)=4 instead of using forward difference at x=2; Incorrect interval selection
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Marking points
M1 · 1 mark · M1: Attempts to find the average rate of change using points on either side of x=2, e.g., (12-6)/(3-2) or (6-2)/(2-1).
M1 · 1 mark · M1: Clearly shows calculation of difference quotient.
A1 · 1 mark · A1: Correctly obtains the answer 6.
Worked solution
Gradient at .