JEE Main 2016 — Application Of Derivatives Question with Solution
From: JEE Main 2016 (Online) 10th April Morning Slot
Question
Let f(x) = sin4x + cos4 x. Then f is an increasing function in the interval :
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
f(x) = sin4x + cos4x
f'(x) = 4sin3x cosx + 4cos3x ( sinx)
= 4sinx cosx (sin2x cos2x)
= 2sin2x cos2x
= sin4x
As, f(x) is increasing function when f'(x) > 0
sin4x > 0
sin4x < 0
< 4x < 2
x
f'(x) = 4sin3x cosx + 4cos3x ( sinx)
= 4sinx cosx (sin2x cos2x)
= 2sin2x cos2x
= sin4x
As, f(x) is increasing function when f'(x) > 0
sin4x > 0
sin4x < 0
< 4x < 2
x
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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.