Q2 of 64 Page 10

Is every differentiable function continuous?

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.


More from this chapter

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12

Is |sin x| differentiable? What about cos |x|?

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Define differentiability of a function at a point.

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Is every continuous function differentiable?

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Give an example of a function which is continuous but not differentiable at a point.