Statement A f(x)=2x3−9x2+12x−3 . . . (i) f′(x)=6x2−18x+12 . . . (ii) For increasing function, f′(x)>0 ∴6(x2−3x+2)>0 ⇒6(x−2)(x−1)>0 ⇒x<1 and x>2 ∴f(x) is increasing outside the interval (1,2), therefore it is true statement. From Eq. (ii) f′(x)=6x2−18x+12 for decreasing f′(x)<0 ⇒6(x−2)(x−1)<0 ⇒x>1 and x<2 ∴f(x) is decreasing in (1,2). ∴A and R are both true, but R is not the correct reason.