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

a=-ω2x =ω2x (numerically) Rate of change of acceleration.dadt=ω2dxdt=ω2v =ω3A2-x2For da/dt to be maximum, x2 should be minimum i.e., x = 0 and  For da/dt to be minimum x2 should be maximum i.e., x = ± a.