Let S be the set of all twice differentiable functions f from \mathbb{R} to \mathbb{R} such that \frac{d^2 f}{d x^2}(x)>0 for all x \in(-1,1). For f \in S, let X_f be the number of points x \in(-1,1) for which f(x)=x. Then which of the following statements is(are) true? [JEE Adv 2023 P2]

There exists a function f \in S such that X_f=0

For every function f \in S, we have X_t \leq 2

There exists a function f \in S, such that X_t=2

There does NOT exist any function f in S such that X_f=1

Differentiation

Section: Mathematics

Question : 1 of 9

Marks: +1, -0

Let S be the set of all twice differentiable functions f from ℝ to ℝ such that ‌

d2f

dx2

(x)>0 for all x∈(−1,1). For f∈S, let Xf be the number of points x∈(−1,1) for which f(x)=x. Then which of the following statements is(are) true?

[JEE Adv 2023 P2]

Go to Question:

Next Question