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Match List-I with List-II The function $f(x) = 2x^3 - 15x^2 +36x +5$ for $x ∈ [2,5]$ has
Choose the correct answer from the options given below: |
(A)-(I), (B)-(II), (C)-(III), (D)-(IV) (A)-(II), (B)-(I), (C)-(IV), (D)-(III) (A)-(II), (B)-(IV), (C)-(I), (D)-(III) (A)-(II), (B)-(III), (C)-(IV), (D)-(I) |
(A)-(II), (B)-(IV), (C)-(I), (D)-(III) |
The correct answer is Option (3) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
$f(x)=2x^3-15x^2+36x+5$ 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. |
