NTA Abhyas JEE Main2020MathematicsContinuity and DifferentiabilityPractice
Consider the function f x = x 3 - x x 2 - 6 x + 5 , ∀ x ∈ R , then f x is
Options
- Adiscontinuous at x = 1
- Bdiscontinuous at x = 5
- Cnon differentiable at x = 1
- Dnon differentiable at x = 5
Correct answer
D. non differentiable at x = 5
Step-by-step solution
f x = x 3 - x x - 1 x - 5 = x x + 1 x - 1 x - 1 x - 5 f x = x 3 - x x 2 - 6 x + 5 x ∈ - ∞ , 1 ∪ 5 , ∞ - x 3 - x x 2 - 6 x + 5 x ∈ 1,5 ∵ x 3 - x , x 2 - 6 x + 5 both are continuous ∀ x ∈ R ∴ f x is also continuous ∀ x ∈ R Now, f ' x = x 3 − x 2 x − 6 + x 2 − 6 x + 5 3 x 2 − 1 x ∈ − ∞ , 1 ∪ 5 , ∞ − x 3 − x 2 x − 6 − x 2 − 6 x + 5 3 x 2 − 1 x ∈ 1 , 5 Now, che