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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? Correct Answer 1 only

Concept:

Differentiable Functions:

  • If a graph has a sharp corner at a point, then the function is not differentiable at that point.
  • If a graph has a break at a point, then the function is not differentiable at that point.
  • If a graph has a vertical tangent line at a point, then the function is not differentiable at that point.

 

Calculation:

Givne that,

f(x) = |x| - 1     ----(1)

Step: 1

Additional Information 

  • Differentiable functions are those functions whose derivatives exist.
  • If a function is differentiable, then it is continuous.
  • If a function is continuous, then it is not necessarily differentiable.
  • The graph of a differentiable function does not have breaks, corners, or cusps.

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