Let f(x) = 3^ (x^ 2 - 2)^ 3 + 4 , x R. Then which of the following statements are true ? P : x = 0 is a point of local minima of f Q : x = 2 is a point of inflection of f R : f' is increasing for x > 2

JEE Main 2022 Mathematics question

Mathematics Application of Derivatives JEE Main 2022

Let + 4}, x R. Then which of the following statements are true ? P : x = 0 is a point of local minima of f Q : is a point of inflection of f R : is increasing for

(1)Only P and Q
(2)Only P and R
(3)Only Q and R
(4)All, P, Q and RCorrect

Answer: (4)

Solution

, so ln 3. The sign of is the sign of x: negative for x < 0 (except at where it vanishes) and positive for x > 0, so x = 0 is a point of local minimum (P is true). Writing = k·g(x)

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Question ID VK-035155