JEE Main 2016MathematicsApplication of DerivativesHardMCQ

JEE Main 2016 — Application of Derivatives Question with Solution

JEE Main 2016 (10 Apr Online)

Question

Let fx=sin4⁡x+cos4⁡x. Then, f is an increasing function in the interval:

Choose an option

Show full solutionCorrect option: C
Correct answer
C ] π 4 , π 2 [

Step-by-step explanation

fx=sin4⁡x+cos4⁡x

f′x=4sin3⁡xcos⁡x+4cos3⁡x-sin⁡x

=4sin⁡xcos⁡xsin2⁡x-cos2⁡x

= -2sin⁡2xcos⁡2x

= -sin⁡4x

fx, is increasing when f′x>0

⇒ -sin⁡4x>0

⇒ sin⁡4x<0

⇒π<4x<2π

⇒π4<x<π2
⇒ x ∈π4,π2

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Application of Derivatives chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2016, 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.