NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice
Which of the following functions satisfies all conditions of the Rolle’s theorem in the intervals specified?
Options
- Af x = x 1 3 , x ∈ - 2,3
- Bf x = sin x , x ∈ - π , π 6
- Cf x = ln x 2 + a b x a + b , x ∈ a , b , 0 < a < b
- Df x = e x 2 - x , x ∈ 0,4
Correct answer
C. f x = ln x 2 + a b x a + b , x ∈ a , b , 0 < a < b
Step-by-step solution
f x = x 1 3 is not differentiable at x = 0 For f x = sin ⁡ x ,   f - π ≠ f π 6 For f x = ln ⁡ x 2 + a b x a + b f a = f b = ln ⁡ 1 = 0 Also, it is continuous in a , b and differentiable in a , b . Hence, Rolle’s Theorem is applicable. For f x = e x 2 - x ,   f 0 ≠ f 4