Let S be the set of all twice differentiable functions f from R to R such that d^2f dx^2 (x) > 0 for all x (-1, 1). For f S, let X_f be the number of points x (-1, 1) for which f(x) = x. Then which of the following statements is(are) true?

JEE Advanced 2023 Mathematics question

Mathematics Application of Derivatives JEE Advanced 2023

Let be the set of all twice differentiable functions from to such that for all . For , let be the number of points for which . Then which of the following statements is(are) true?

(A)There exists a function such that Correct
(B)For every function , we have Correct
(C)There exists a function such that Correct
(D)There does **NOT** exist any function in such that

Answer: (A),(B),(C)

Solution

has on , so it is strictly convex there and can have at most two zeros – (B) true. Examples: gives $g =

See the full step-by-step solution

Create a free account to read the complete working, and practise questions like this in a timed test.

Create a free account

Question ID VK-034119