anonymous
  • anonymous
It's true that if f is differentiable in (a,b) then f is continuous in (a,b). But would it be correct to say that if f is differentiable in (a,b) then f is continuous in [a,b] ?
MIT 18.01 Single Variable Calculus (OCW)
jamiebookeater
  • jamiebookeater
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henriquerb
  • henriquerb
I don't think it's necessarily true. I mean, it could be true, but could also be false.
anonymous
  • anonymous
All differentiable functions are continuous on that same interval.SO THE FIRST STATEMENT IS TRUE. but NOT all continuous functions are differentiable .SO FOR THE SECOND STATEMENT I THINK IT IS FALSE.
anonymous
  • anonymous
Pasta is right. Just consider most rational power functions and the absolute value function.

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anonymous
  • anonymous
If f(x) is differentiable at (a,b), then it has to be continuous the the same point. But, it is not necessary that every continuous function is differentiable. For example: f(x) = |x| Hence we conclude that 1) Differentiability implies continuity 2) Continuity does not imply differentiability.

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