For the function $f(x) = 2x^3-9x^2+12x-5, x \in [0, 3]$, match List-I with List-II.
|
List-I |
List-II |
|
(A) Absolute maximum value |
(I) 3 |
|
(B) Absolute minimum value |
(II) 0 |
|
(C) Point of maxima |
(III) -5 |
|
(D) Point of minima |
(IV) 4 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
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)