JEE Main 2026 — Application of Derivatives Question with Solution
JEE Main 2026 (24 January Shift 1)
Question
Let be the largest interval in which the function , is strictly decreasing. Then the local maximum value of the function , is
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Show full solutionCorrect answer: 4
Correct answer
4
Step-by-step explanation
For , analyze in two regions.
For :
, so (increasing).
For :
, so .
For :
(decreasing).
For :
(increasing).
Largest decreasing interval is , so .
For :
gives , so .
Since , is maximum.
For :
, so (increasing).
For :
, so .
For :
(decreasing).
For :
(increasing).
Largest decreasing interval is , so .
For :
gives , so .
Since , is maximum.
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This is a previous-year question from JEE Main 2026, 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.