Write down the equation of the curve on which all these maximum and minimum points lie.

Sketch this curve on the slope field.

The solution to the differential equation that passes through the point $(0, -2)$ has both a local maximum point and a local minimum point.

On the slope field, sketch the solution to the differential equation that passes through $(0, -2)$.

$x^2+\frac{y}{2}=0 \left(y=-2x^2\right)$           A1

[1 mark]

$y=-2x^2$ drawn on diagram (correct shape with a maximum at $(0,0)$)        A1

[1 mark]

correct shape with a local maximum and minimum, passing through $(0, -2)$         A1

local maximum and minimum on the graph of $y=-2x^2$         A1

[2 marks]

This question was very poorly done and frequently left blank. Few candidates understood the connection between the differential equation and maximum and minimum points. Even when the equation $\frac{\text{d}y}{\text{d}x}=0$ was correctly solved, it was rare to see the curve correctly drawn on the slope field. Some were able to draw a solution to the differential equation on the slope field though often not through the given initial condition.