Verified Solution • 2025–26 Session moderate

QJEEM16Ma0712: JEE Main 2016 Mathematics - Class 12 JEEM16Ma0712 Solution: Let f(x) = sin 4 x + cos 4 x. Then f is an increasing function…

Let f(x) = sin4x + cos4 x. Then f is an increasing function in the interval :

Multiple Choice Options

  • A ]0,π4[] 0, \frac{\pi}{4}[
  • B ]π4,π2[] \frac{\pi}{4}, \frac{\pi}{2}[
  • C ]π2,5π8[] \frac{\pi}{2}, \frac{5 \pi}{8}[
  • D ]5π8,3π4[] \frac{5 \pi}{8}, \frac{3 \pi}{4}[

Step-by-Step Verified Solution

f(x) = sin4x + cos4x

∴\therefore    f'(x) = 4sin3x cosx + 4cos3x ( −- sinx)

= 4sinx cosx (sin2x −- cos2x)

= −- 2sin2x cos2x

= −- sin4x

As, f(x) is increasing function when f'(x) > 0

⇒\Rightarrow     −- sin4x > 0

⇒\Rightarrow    sin4x < 0

∴\therefore     π\pi < 4x < 2 π\pi

{\pi \over 4} &lt; x &lt; {\pi \over 2}

∴\therefore    x ∈\in (π4,π2)\left( {{\pi \over 4},{\pi \over 2}} \right)

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