The interval in which f(x)=2x^3-9x^2+12x+1 is decreasing is :

The correct answer is Option (2) → [1, 2]

$f(x)=2x^3-9x^2+12x+1$

$f'(x)=6x^2-18x+12=0$

$⇒x^2-3x+2=0$

so $x^2-2x-x+2=0$

$(x-2)(x-1)=0⇒x=1,2$

f(x) decreasing in [1, 2]