DP Mathematics: Applications and Interpretation Questionbank

Find the equation of $L_1$, giving your answer in the form $y=mx+c$.

For the two solutions given, the local maximum points lie on the straight line $L_2$.

Find the equation of $L_2$.

Calculate the value of $\frac{dy}{dx}$ at the point $(0, 1)$.

Sketch, on the first graph, a curve that represents the points where $\frac{dy}{dx}=0$.

(i)   sketch the solution curve that passes through the point $(0, 0)$.

(ii)  sketch the solution curve that passes through the point $(0, 0.75)$.

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

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 $(0, -2)$.

Sketch this curve on the slope field.