Question:
Consider the following statements in respect of f(x) = |x| – 1
1. f(x) is continuous at x = 1.
2. f(x) is differentiable at x = 0.
Which of the above statements is/are correct?
Consider the following statements in respect of f(x) = |x| – 1 1. f(x) is continuous at x = 1. 2. f(x) is differentiable at x = 0. Which of the above statements is/are correct?
Options:
- only 2
- Neither 1 nor 2
- Both 1 and 2
- only 1
- only 2
- Neither 1 nor 2
- Both 1 and 2
- only 1
Correct Answer: d)
Explanation:
‘ Gi√en, f(x) = x – 1
‘ Since, modulus function is continuous.
1 = f(x) is continuous at x = 1 and x is not differentiable if x = 0
‘ f(x) = x – 1 is not differentiable at x = 0
Hence, statement (I) is correct and (II) is false.
‘ Gi√en, f(x) = x – 1
‘ Since, modulus function is continuous.
1 = f(x) is continuous at x = 1 and x is not differentiable if x = 0
‘ f(x) = x – 1 is not differentiable at x = 0
Hence, statement (I) is correct and (II) is false.