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NTA Abhyas JEE Main2020MathematicsContinuity and DifferentiabilityPractice

Which of the following is a correct statement?

Options

  1. AContinuity at x = a is sufficient for differentiability at x = a
  2. BDifferentiability at x = a is sufficient for continuity at x = a
  3. CExistence of limit at x = a is sufficient for continuity at x = a
  4. DDifferentiability at x = a is necessary for existence of tangent at x = a

Correct answer

B. Differentiability at x = a is sufficient for continuity at x = a

Step-by-step solution

If f x is differentiable at x = a , then f x is also continuous at x = a Hence, differentiability at x = a is sufficient for continuity at x = a

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