EAMCET Engineering 2005 Solved Paper

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.