NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

If f x 2 - 4 x + 3 > 0 , ∀ x ∈ 2 , 3 , then g x = f sin ⁡ x is increasing in

Options

Ax ∈ 0 , π
Bx ∈ 0 , π 2
Cx ∈ π , 5 π 4
Dx ∈ 3 π 2 , 2 π

Correct answer

D. x ∈ 3 π 2 , 2 π

Step-by-step solution

x 2 - 4 x + 3 = x - 2 2 - 1 If x ∈ 2,3 , then x 2 - 4 x + 3 ∈ - 1,0 Now, g ′ x = f ′ sin x . cos x For g x to be increasing sin ⁡ x ∈ - 1,0 and cos ⁡ x > 0 ⇒ x ∈ 3 π 2 , 2 π

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