JEE Main 2015MathematicsApplication of DerivativesMediumMCQ

JEE Main 2015 — Application of Derivatives Question with Solution

JEE Main 2015 (10 Apr Online)

Question

If Rolle's theorem holds for the function fx=2x3+bx2+cx, x∈-1,1 at the point x=12, then 2b+c is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C-1

Step-by-step explanation

Since, Rolle's theorem is satisfied in [-1, 1] and corresponding to x=12 we have   f(−1)=f(1)   &   f'12=0

So,  −2+b−c=2+b+c

⇒ c=−2

Further f'x=6x2+2bx+c

Put x=12

So f'12=32+b+c=0  

⇒b=12

Hence, 2b+c=-1

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About this question

This is a previous-year question from JEE Main 2015, 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.