(a) Prove: If f (x) exists for each x in (a, b), then both fand f are continuous on (a

Chapter 2, Problem 74

(choose chapter or problem)

(a) Prove: If $f^{\prime \prime}(x)$ exists for each x in $(a, b)$, then both $f$ and $f^{\prime}$ are continuous on $(a, b)$.

(b) What can be said about the continuity of $f$ and its derivatives if $f^{(n)}(x)$ exists for each x in $(a, b)$?

Equation Transcription:

${f}^{''}(x)$

$(a,b)$

$f$

${f}^{'}$

${f}^{(n)}(x)$

Text Transcription:

f''(x)

(a,b)

f^(n) (x)

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