NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice
For the function f x = sin 3 x - 3 sin x + 4 ∀ x ∈ 0 , π 2 , which of the following is true?
Options
- AGreatest value of the function is 2 π
- BGreatest value of the function is 4
- CRolle’s Theorem is applicable to f x in x ∈ 0 , π 2
- DLMVT is not applicable to f x in x ∈ 0 , π 2
Correct answer
B. Greatest value of the function is 4
Step-by-step solution
Let, sin ⁡ x = t ∈ 0,1 ∴ f t = t 3 - 3 t + 4 Now, f ′ t = 3 t 2 − 3 = 3 t - 1 t + 1 ∴ f ′ t ≤ 0  ∀ t ∈ 0 , 1 ∴ max ⁡ f t = 0 - 0 + 4 = 4 Also, f x is continuous in 0,1 and differentiable in 0,1 , hence LMVT is applicable. But, f 0 ≠ f 1 , hence Rolle’s theorem is not applicable