While a particle executes simple harmonic motion, the rate of change of acceleration is maximum and minimum, respectively at

$\mathrm{a}=-{\mathrm{\omega }}^2\mathrm{x} ={\mathrm{\omega }}^2\mathrm{x}$ (numerically) Rate of change of acceleration.
$$\begin{gathered} \frac{\mathrm{da}}{\mathrm{dt}}={\mathrm{\omega }}^2\frac{\mathrm{dx}}{\mathrm{dt}}={\mathrm{\omega }}^2\mathrm{v} \\ ={\mathrm{\omega }}^3\sqrt{{\mathrm{A}}^2-{\mathrm{x}}^2} \end{gathered}$$
For da/dt to be maximum, ${\mathrm{x}}^2$ should be minimum i.e., x = 0 and 
 For da/dt to be minimum ${\mathrm{x}}^2$ should be maximum i.e., x = ± a.