Let f(x) is increasing and double differentiable function everywhere such that f(x) = x has 3 distinct root α , β and γ ( α 0 ∀ x ∈ (– ∞ , β ) and f”(x) < 0 ∀ x ∈ ( β , ∞ ) and f”( β ) = 0, then find h(x) (ii) If f(x) ≥ x ∀ x ∈ (– ∞ , β ] and f(x) ≤ x ∀ x ∈ [ β , ∞ ) then find h(x)

Let f(x) is increasing and double differentiable function e…

Maths Functions, Limits, Continuity and Differentiability General Subjective Type

Published on: August 14, 2026

Let f(x) is increasing and double differentiable function everywhere such that f(x) = x has 3 distinct root α , β and γ ( α < β < γ ). h(x) =

(i) If f”(x) > 0 ∀ x ∈ (– ∞ , β ) and f”(x) < 0 ∀ x ∈ ( β , ∞ ) and f”( β ) = 0, then find h(x)

(ii) If f(x) ≥ x ∀ x ∈ (– ∞ , β ] and f(x) ≤ x ∀ x ∈ [ β , ∞ ) then find h(x)

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The correct answer is:

CHECK THE SOLUTION.

(i) h(x) =

(ii) h(x) =

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