UPSC Maths Optional 2025 PYQ: Functional Equation f(x + y)=f(x)f(y), f′(0)=2 | GR IAS Academy
Автор: GR IAS ACADEMY
Загружено: 2026-03-01
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Problem (UPSC Mathematics Optional):
Given that,
f(x + y) = f(x)f(y) for all real x, y
f(x) ≠ 0 for any real x
f′(0) = 2
Show that f′(x) = 2f(x) for all real x.
Hence find f(x).
In this video, we solve an important Functional Equation combined with Differential Calculus, a frequently asked concept in UPSC Mathematics Optional.
This problem helps you understand:
• Functional equations of exponential type
• Use of derivative at a point
• Connection between algebraic functional equations and differential equations
• How to rigorously prove f′(x) = 2f(x)
This topic is highly important for:
✔ UPSC CSE Mathematics Optional
✔ University B.Sc / M.Sc Mathematics
✔ Real Analysis & Calculus preparation
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