The sum of absolute maximum and absolute minimum values of the function f(x) = |2x^ 2 + 3x − 2| + sin x cos x in the interval [0, 1] is :

JEE Main 2022 Mathematics question

Mathematics Application of Derivatives JEE Main 2022

The sum of absolute maximum and absolute minimum values of the function − 2| + sin x cos x in the interval [0, 1] is :

(1)
(2) sin(1)Correct
(3)
(4)2 + sin(1/2)cos(1/2)

Answer: (2)

Solution

f(x) = |(2x − 1)(x + 2)| + (sin 2x)/2. On [0, 1/2], f = (1 − 2x)(x + 2) + (sin 2x)/2, with = −4x − 3 + cos 2x < 0. For , + cos 2x > 0. So the minimum is at x = 1/2, where f = (sin 1)/2. The

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Question ID VK-024141