f(x)=2x3−9ax2+12a2x+1 f′(x)=6x2−18ax+12a2 f′′(x)=12x−18a For max. or min. 6x2−18ax+12a2=0 ⇒x2−3ax+2a2=0 ⇒x=a or x=2a. At x=a f′′(a)=12a−18a=−6a<0 At x=a maximum As f′′(a)<0. At x=2a f′′(a)=24a−18a=6a>0 At x=2a minimum As f′(2a)>0. ∴p=a and q=2a As per question p2=q ∴a2=2a ⇒a(a−2)=0 ∴a=0,2 but a>0, therefore, a=2.