Answer :

Yes, if a function is differentiable at a point then it is necessarily continuous at that point.

Let f(x) be a function differentiable at x = c.

Then,

exists finitely

Let

To prove that f(x) is continuous at x = c, it is sufficient to show that

Hence, f(x) is continuous at x = c.

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

RELATED QUESTIONS :

Show that of all Mathematics - Board Papers

Find the value ofMathematics - Board Papers

If x sin (a + y) Mathematics - Exemplar

The function f(x)Mathematics - Exemplar

Show that of all Mathematics - Board Papers

If the function fMathematics - Board Papers

Find <img wMathematics - Exemplar

Let f(x) = |sinx|Mathematics - Exemplar

The derivative ofMathematics - Exemplar