Question

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

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

Answer 1

Answer: (D)

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

Answer 2

Differentiate $f(x) = 2x^3 - 9x^2 + 12x - 5$ to find $f'(x) = 6x^2 - 18x + 12$.
Solve $f'(x) = 0$ to find critical points within the interval $[0, 3]$.
Evaluate $f(x)$ at the endpoints $x = 0$ and $x = 3$, and at the critical points, to determine the absolute maximum and minimum values.