JEE Main 2022MathematicsApplication of DerivativesHardMCQ

JEE Main 2022 — Application of Derivatives Question with Solution

JEE Main 2022 (26 Jun Shift 1)

Question

Let fx=2cos-1x+4cot-1x-3x2-2x+10,x∈-1,1. If a,b is the range of the function, then 4a-b is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B11-π

Step-by-step explanation

Given fx=2cos-1x+4cot-1x-3x2-2x+10

f'x=-21-x2-41+x2-6x-2

=-211-x2+21+x2+3x+1

f'x<0 ⇒fx is a decreasing function

Now f1=π+5 and f-1=5π+5

So, range: a,b≡π+5,5π+5

a=π+5, b=5π+5⇒4a-b=11-π

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About this question

This is a previous-year question from JEE Main 2022, 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.