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Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If a function is continuous at a point, then it is differentiable at that point.

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Step-by-step explanation:

If a Function is differentiable at a point c, it is also continuous at that point.

but be careful, to not assume that the inverse statement is true if a fuction is Continuous it doest not mean it is necessarily differentiable, it must satisfy the two conditions.

  • the function must have one and only one tangent at x=c
  • the fore mentioned tangent cannot be a vertical line.

                                          And

If function is differentiable at a point x, then function must also be continuous at x. but The converse does not hold, a continuous function need not be differentiable.

  • For example, a function with a bend, cusp, or vertical tangent may be continuous, but fails to be differentiable at the location of the anomaly.

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