NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice
For the function f x = sin x + 2 cos x , ∀ x ∈ 0,2 π , we obtain
Options
- Aa local point of maxima at x = α , where α is in 1 s t quadrant
- Ba local point of maxima at x = α , where α is in 3 r d quadrant
- Ca local point of minima at x = α , where α is in 1 s t quadrant
- Da local point of minima at x = α , where α is in 2 n d quadrant
Correct answer
A. a local point of maxima at x = α , where α is in 1 s t quadrant
Step-by-step solution
f x = sin ⁡ x + 2 cos ⁡ x ,   ∀ x ∈ 0,2 π f ' x = cos ⁡ x - 2 sin ⁡ x ⇒ f ' x changes its sign from positive to negative at x = t a n - 1 1 2 ∈ 0 , π 2 So at this point, local maxima occurs ⇒ f ' x changes its sign from negative to positive at x = π + t a n - 1 1 2 ∈ π , 3 π 2 So at this point, local minima occurs