NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice
For f x = 1 + sin x : x < 0 x 2 - x + 1 : x ≥ 0 , then the incorrect statement is
Options
- Ax = 0 is a point of local maxima
- B2 f x = 1 has no real solution in x ∈ 0 , ∞
- Cf x is increasing in x ∈ 2 , π
- Df x is decreasing in x ∈ 0 , 1 2
Correct answer
D. f x is decreasing in x ∈ 0 , 1 2
Step-by-step solution
Clearly, x = 0 is local maximum If f x = 1 2 ⇒ x 2 - x + 1 = 1 2 ⇒ x 2 - x + 1 2 = 0 D = 1 - 4 1 2 < 0 ⇒ No real solution Also, f x is increasing ∀ x ∈ 1 2 , ∞ and in 2 , π , but decreasing in 0 , 1 2