anonymous
  • anonymous
Why did we have to say f is continuous on [a,b] and differentiable on (a,b) when we could just say f is differentiable on [a,b] (which implies f is continuous on [a,b])
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
I see that a lot in Calculus
anonymous
  • anonymous
and in Real Analysis
anonymous
  • anonymous
The first way says that its continuous on the whole interval but only differentiable on the open interval, so not at the end points. However, the second way "f is differentiable on [a,b] => f is continuous on [a,b]" is saying that its both differentiable and continuous on the whole interval. As for why it matters that its differentiable only on the open interval, not the closed, I can't say.

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