JEE Main 2022MathematicsApplication of DerivativesMediumMCQ

JEE Main 2022 — Application of Derivatives Question with Solution

JEE Main 2022 (29 Jun Shift 2)

Question

Let f: R→R be a function defined by fx=x-3n1x-5n2, n1, n2∈N. The, which of the following is NOT true?

Choose an option

Show full solutionCorrect option: C
Correct answer
CFor n1=3, n2=5, there exists α∈3, 5 where f attains local maxima.

Step-by-step explanation

Given,

fx=x-3n1x-5n2

Differentiating the function to get maxima and minima, we get

f'x=x-3n1-1x-5n2-1n1+n2x-5n1+3n2n1+n2

Now checking the option, we get

Option (3) is incorrect since

for n1=3, n2=5

f'x=8x-32x-54x-308

minima at x=308.

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About this question

This is a previous-year question from JEE Main 2022, 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.