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Limits, Continuity and Differentiability

Section: Mathematics

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Question : 2

Total: 51

Let ℝ denote the set of all real numbers. Define the function f:ℝ⟶ℝ by f(x)={

2−2x2−x2sin‌‌

‌ if ‌x≠0

Then which one of the following statements is TRUE?

[JEE Adv 2025 P1]

The function f is NOT differentiable at x=0
There is a positive real number δ, such that f is a decreasing function on the interval (0,δ)
For any positive real number δ, the function f is NOT an increasing function on the interval (−δ,0)
x=0 is a point of local minima of f

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