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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] ?
 one year ago
 one year ago
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] ?
 one year ago
 one year ago

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henriquerbBest ResponseYou've already chosen the best response.0
I don't think it's necessarily true. I mean, it could be true, but could also be false.
 one year ago

pastaBest ResponseYou've already chosen the best response.1
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.
 one year ago

L.T.Best ResponseYou've already chosen the best response.0
Pasta is right. Just consider most rational power functions and the absolute value function.
 one year ago

AbbasBagwalaBest ResponseYou've already chosen the best response.0
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.
 one year ago
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