Let ℝ denote the set of all real numbers. Let f : ℝ → ℝ be defined by f(x) = cases 6x + x 2x + x & if x 0, 7 3 & if x = 0. cases Then which of the following statements is (are) TRUE?

JEE Advanced 2025 Mathematics question

Let ℝ denote the set of all real numbers. Let f : ℝ → ℝ be defined by

f(x) =

Then which of the following statements is (are) TRUE?

Answer: (B),(C),(D)

, with , (so f is continuous). Near 0, , so f(x) > f(0): x = 0 is a local minimum (B true, A false). , so the other

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Question ID VK-035473