JEE Main 2020MathematicsApplication of DerivativesHardMCQ

JEE Main 2020 — Application of Derivatives Question with Solution

JEE Main 2020 (08 Jan Shift 1)

Question

Let fx=xcos-1⁡-sin⁡x,x∈-π2,π2, then which of the following is true?

Choose an option

Show full solutionCorrect option: D
Correct answer
Df' is decreasing in -π2,0 and increasing in 0,π2

Step-by-step explanation

f'x=xπ-cos-1sinx=x(ππ2-sin-1sinx=xπ2+x
fx=xπ2+xx≥0xπ2-xx<0
f'x=π2+2xx≥0π2-2xx<0
f'x is increasing in 0, π2 and decreasing in -π2, 0.

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About this question

This is a previous-year question from JEE Main 2020, 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.