June 2025 Paper 3 Q8

OCR MEICurrent spec3 marksDifferentiation

8 The diagram below shows the graph of \(y\) as a function of \(x\).

Point D is the fixed point on the graph where \(x = 10\).
Point E is the point on the graph where \(x = 10 + h\) where \(h\) denotes a small increase in \(x\).
The values of \(y\) at points D and E differ by \(k\).

The value of the gradient of chord DE is \(\dfrac{k}{h}\).

S-shaped graph of y against x levelling off; chord DE with horizontal step h and vertical step k marked

The screenshot below shows a spreadsheet used to find the gradient of DE for different values of \(h\). The contents of some of the cells are not shown in the screenshot.

ABCDE
1\(h\)10+\(h\)\(y\)\(k\)gradient
21111992.8197.5937197.594
30.11817.5422.33784
40.0110.011797.462.259142225.914
50.00110.0011795.430.226167226.167
60.000110.00011795.220.022619226.192
70.0000110.000011795.20.002262226.195
8
(a) Write down the value for cell B3. [1]
(b) Find the value for cell E3. Give your answer to 3 decimal places. [1]
(c) Deduce, to 1 decimal place, the value of the gradient of the graph at D. [1]
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