9709 P11 - Jun 2024 - Q4 - 3 marks
10091
The curve is \(y=f(x)=(2x-1)\sqrt{3x-2}-2\). Its points are listed below; the y-coordinates are rounded to 5 decimal places.
| Point | x | y |
|---|---|---|
| A | 2 | 4 |
| B | 2.0001 | k |
| C | 2.001 | 4.00625 |
| D | 2.01 | 4.06261 |
| E | 2.1 | 4.63566 |
| F | 3 | 11.22876 |
(a) Find k to 5 decimal places. [1]
The gradients of AB, AC, AD and AF are 6.2501, 6.2511, 6.2608 and 7.2288 respectively.
(b) Calculate the gradient of AE to 4 decimal places. [1]
(c) Estimate f′(2). [1]
