Date | May 2021 | Marks available | 2 | Reference code | 21M.1.AHL.TZ1.15 |
Level | Additional Higher Level | Paper | Paper 1 | Time zone | Time zone 1 |
Command term | Find | Question number | 15 | Adapted from | N/A |
Question
The diagram shows the slope field for the differential equation
dydx=sin(x+y), -4≤x≤5, 0≤y≤5dydx=sin(x+y), −4≤x≤5, 0≤y≤5.
The graphs of the two solutions to the differential equation that pass through points (0, 1) and (0, 3) are shown.
For the two solutions given, the local minimum points lie on the straight line L1.
Find the equation of L1, giving your answer in the form y=mx+c.
For the two solutions given, the local maximum points lie on the straight line L2.
Find the equation of L2.
Markscheme
sin(x+y)=0 A1
⇒x+y=0 (M1)
(the equation of L1 is) y=-x A1
[3 marks]
x+y=π OR y=-x+π (M1)A1
[2 marks]