JEE Main 2024 Mathematics question

Mathematics Application of Derivatives JEE Main 2024

Consider the function f : (0, 2) → R defined by and the function g(x) defined by . Then,

(A)g is not continuous for all x ∈ (0, 2)
(B)g is continuous and differentiable for all x ∈ (0, 2)
(C)g is continuous but not differentiable at x = 1Correct
(D)g is neither continuous nor differentiable at x = 1

Answer: (C)

Solution

f′(x) = (x² − 4)/(2x²) < 0 on (0, 2), so f is decreasing and min f(t) over 0 < t ≤ x is f(x). So g(x) = f(x) for x ∈ (0, 1] and g(x) = 3/2 + x

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Question ID VK-016630