Let f x = 3 sin 4 x + 10 sin 3 x + 6 sin 2 x - 3 , x ∈ - π 6 , π 2 . Then, f is :

Let fx=3sin4x+10sin3x+6sin2x-3, x∈-π6,π2. Then, f is :
  1. increasing in -π6,π2
  2. decreasing in 0,π2
  3. increasing in -π6,0
  4. decreasing in -π6,0

Solution

fx=3sin4x+10sin3x+6sin2x-3, x∈-π6,π2

⇒f'x=12sin3xcosx+30sin2xcosx+12sinxcosx

=6sinxcosx2sin2x+5sinx+2

=6sinxcosx(2sinx+1)(sinx+2)

From wavy curve, we can say f'(x)<0 in -π6,0

So, the function is Decreasing in -π6,0

Asked in: JEE Main 2021 (25 Jul Shift 1)

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