JEE Main 2024MathematicsApplication of DerivativesEasyMCQ

JEE Main 2024 — Application of Derivatives Question with Solution

JEE Main 2024 (01 Feb Shift 1)

Question

If 5fx+4f1x=x2−2,∀x≠0 and y=9x2fx, then y is strictly increasing in:

Choose an option

Show full solutionCorrect option: B
Correct answer
B−15,0∪15,∞

Step-by-step explanation

Given: 5fx+4f1x=x2-2   ...i

Replacing x by 1x.

⇒5f1x+4fx=1x2-2   ...ii

Using, i×5-ii×4

⇒25fx+20f1x-16fx-20f1x=5x2-10-4x2+8

⇒9fx=5x2-4x2-2

Now, y=9fx×x2

⇒y=5x2-2-4x2×x2

⇒y=5x4-2x2-4

⇒y'=20x3-4x

⇒y'=4x5x2-1

For function to be increasing y'>0

⇒x∈-15,0∪15,∞

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About this question

This is a previous-year question from JEE Main 2024, covering the Application of Derivatives 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.