Match List-I with List-II
The function $f(x) = 2x^3 - 15x^2 +36x +5$ for $x ∈ [2,5]$ has
|
List-I |
List-II |
|
(A) absolute maximum value |
(I) 5 |
|
(B) absolute minimum value |
(II) 60 |
|
(C) point of absolute maxima |
(III) 3 |
|
(D) point of absolute minima |
(IV) 32 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
|
List-I |
List-II |
|
(A) absolute maximum value |
(II) 60 |
|
(B) absolute minimum value |
(IV) 32 |
|
(C) point of absolute maxima |
(I) 5 |
|
(D) point of absolute minima |
(III) 3 |
$f(x)=2x^3-15x^2+36x+5$ on $[2,5]$
$f'(x)=6x^2-30x+36=6(x^2-5x+6)=6(x-2)(x-3)$
Critical points: $x=2,\;x=3$ (both in the interval)
Evaluate:
$f(2)=2(8)-15(4)+36(2)+5=16-60+72+5=33$
$f(3)=2(27)-15(9)+36(3)+5=54-135+108+5=32$
$f(5)=2(125)-15(25)+36(5)+5=250-375+180+5=60$
Correct matching: A–II, B–IV, C–I, D–III.