9709 P12 - Jun 2021 - Q3 - 4 marks
87
The equation of a curve is \(y=(x-3)\sqrt{x+1}+3\). The following points lie on the curve. Non-exact values are rounded to 4 decimal places.
| Point | Coordinates |
|---|---|
| A | \((2,k)\) |
| B | \((2.9,2.8025)\) |
| C | \((2.99,2.9800)\) |
| D | \((2.999,2.9980)\) |
| E | \((3,3)\) |
(a) Find k, giving your answer correct to 4 decimal places. [1]
(b) Find the gradient of AE, giving your answer correct to 4 decimal places. [1]
The gradients of BE, CE and DE, rounded to 4 decimal places, are 1.9748, 1.9975 and 1.9997 respectively.
(c) State, giving a reason for your answer, what the values of the four gradients suggest about the gradient of the curve at E. [2]
