JEE Main 2021MathematicsApplication of DerivativesMediumNumerical

JEE Main 2021 — Application of Derivatives Question with Solution

JEE Main 2021 (31 Aug Shift 1)

Question

If R is the least value of a such that the function fx = x2 + ax + 1 is increasing on [1,2] and S is the greatest value of a such that the function f(x) = x2 + ax + 1 is decreasing on [1, 2], then the value of |R-S| is

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Show full solutionCorrect answer: 2
Correct answer
2

Step-by-step explanation

If f'(x)=2x+a≥0∀x∈[1,2]  ⇒a≥-2x∀x∈[1,2]

amin=R=-2 If

amax=S=-4

|R-S|=2

Alternate :

If f(x) is increasing for all x∈[1,2] then

-a2≤1⇒a≥-2⇒R=-2

If f(x) is decreasing for x∈[1,2], then

-a2≥2⇒a≤-4⇒S=-4

|R-S|=2

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About this question

This is a previous-year question from JEE Main 2021, 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.