JEE Main 2026 — Application of Derivatives Question with Solution
JEE Main 2026 (28 January Shift 2)
Question
Let be a differentiable function satisfying and let . If p and q are respectively the points of local minima and local maxima of g, then the value of is equal to .
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Show full solutionCorrect answer: 9
Correct answer
9
Step-by-step explanation
Given .
Differentiating and simplifying:
This reduces to:
Solving the linear ODE :
On solving, we get .
Now,
Sign analysis of :
changes from at → local maxima
changes from at → local minima
Differentiating and simplifying:
This reduces to:
Solving the linear ODE :
On solving, we get .
Now,
Sign analysis of :
changes from at → local maxima
changes from at → local minima
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