JEE Main 2014MathematicsApplication of DerivativesEasyMCQ

JEE Main 2014 — Application of Derivatives Question with Solution

JEE Main 2014 (09 Apr Online)

Question

If the Rolle's theorem holds for the function fx=2x3+ax2+bx in the interval −1,1 for the point c=12, then the value of 2a+b is:

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Show full solutionCorrect option: A
Correct answer
A-1

Step-by-step explanation

Given that the function holds Rolle's theorem in the interval −1,1

⇒ f-1=f1

⇒−2+a−b=2+a+b

⇒b=-2

Now, f'x=6x2+2ax+b

∴  f'12=0⇒6×14+2a×12+b=0

⇒  a=12

⇒ 2a+b=-1

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About this question

This is a previous-year question from JEE Main 2014, 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.