For the function $f(x) = 2x^3-9x^2+12x-5, x \in [0, 3]$, match List-I with List-II.

Choose the correct answer from the options given below:

(A) - (IV), (B) - (III), (C) - (I), (D) - (II)

The correct answer is Option (4) - (A) - (IV), (B) - (III), (C) - (I), (D) - (II)

$f(x) = 2x^3-9x^2+12x-5$

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

$x^2-3x+2=0$

$(x-2)(x-1)=0$

$x=1,2$ → critical points

so $f(0)=-5$ → minima

$f(1)=0$

$f(2)=-1$

$f(3)=4$ → maxima

so (A) - (IV), (B) - (III), (C) - (I), (D) - (II)