JEE Main 2022MathematicsApplication of DerivativesMediumMCQ

JEE Main 2022 — Application of Derivatives Question with Solution

JEE Main 2022 (26 Jul Shift 2)

Question

If the maximum value of a, for which the function fax=tan-12x-3ax+7 is non-decreasing in -π6,π6, is a¯, then fa¯π8 is equal to

Choose an option

Show full solutionCorrect option: A
Correct answer
A8-9π49+π2

Step-by-step explanation

Given fax=tan-12x-3ax+7 is non-decreasing function in -π6,π6, so 

fa'x=21+4x2-3a≥0

i.e. a≤231+4x2min 

Now, maximum value of a is at x=0

i.e. amax=a¯=69+π2

Hence, fa¯π8=tan-1π4-369+π2π8+7

=tan-1π4-9π4π2+9+7=8-9π4π2+9

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 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.