JEE Main 2019 — Application Of Derivatives Question with Solution
From: JEE Main 2019 (Online) 12th January Evening Slot
Question
If the function f given by f(x) = x3 – 3(a – 2)x2 + 3ax + 7, for some aR is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, is :
Choose an option
Show full solutionCorrect option: C
Correct answer
C7
Step-by-step explanation
f '(x) = 3x2 6(a 2)x + 3a
f '(x) 0 x (0, 1]
f '(x) 0 x [1, 5)
f '(x) = 0 at x = 1 a = 5
f(x) 14 = (x 1)2 (x 7)
f '(x) 0 x (0, 1]
f '(x) 0 x [1, 5)
f '(x) = 0 at x = 1 a = 5
f(x) 14 = (x 1)2 (x 7)
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