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COMEDK2016MathematicsContinuity and Differentiability

Which one of the following is not true always?

Options

  1. AIf a function f(x) is continuous at x=a , then _ x a f(x) exists.
  2. BIf f(x) and g(x) are differentiable at x=a , then f(x)+g(x) is also differentiable at x=a .
  3. CIf f(x) is continuous at x=a , then it is differentiable at x=a .
  4. DIf f(x) is not continuous at x=a , then it is not differentiable at x=a .

Correct answer

C. If f(x) is continuous at x=a , then it is differentiable at x=a .

Step-by-step solution

If a function f(x is continuous at x=a) . Then, it may or may not be differentiable at x=a .

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