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 max.and at x=2amin. p2=q a2=2a⇒a=2 or a=0 but a>0, therefore, a=2.
If the function f(x)=2x2−9ax2+12a2x+1, where a>0, attains its maximum and minimum at p and q respectively such that p2=q, then a equals
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