If the functionf(x)=2x3−9ax2+12a2x+1 , where a>0  ,attains its maximum and minimum at p and q respectively such that p2=q , then a equals:

f(x)=2x3−9ax2+12a2x+1 f'(x)=6x2−18ax+12a2 f''(x)=12x−18a ∴f'(x)=0⇒x=a,2a ∴f'(a)<0 and f''(2a)>0 ∴f(a) Has max. at x = a and min. at x = 2a∴p=a,q=2a ∴a2=2a⇒a=2(∵a>0)