JEE Main 2022MathematicsDifferentiationHardNumerical

JEE Main 2022 — Differentiation Question with Solution

JEE Main 2022 (26 Jun Shift 2)

Question

Let f:ℝ→ℝ satisfy fx+y=2xfy+4y(fx,∀x, y∈ℝ. If f2=3, then 14·f'4f'2 is equal to _____.

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Show full solutionCorrect answer: 248
Correct answer
248

Step-by-step explanation

Given, fx+y=2xfy+4y(fx

Put y=2 we get,

fx+2=2x×3+16fx

f'x+2=16f'x+3×2xln2

Now put x=2 we get,

f'4=16f'2+12ln2     …i

Similarly, fy+2=4fy+3×4y

f'4=4f'y+3×4yln4

f'4=4f'2+96ln2     ⋯ii

solving eq. i and ii, we get

f'2=7ln2

from equation i, we get

f'4=124ln2

Now ⇒14×f'4f'2

14×124ln27ln2=248

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About this question

This is a previous-year question from JEE Main 2022, covering the Differentiation chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.