2α+β=8 f′(x)=6x2−18ax+12a2 Critical points f′(x)=0 ⇒6x2−18ax+12a2=0 ⇒(x−a)(x−2a)=0 ⇒x=a,x=2a Now, f"(x)=12x−18a at x=a f"(a)=−6a<0, as a>0 x=a is point of maxima at x=2a f"(2a)=6a>0 x=2a is point of minima ∴α=a,β=2a ∵2α+β=8 2a+2a=8 ⇒a=2