Let f be a function defined on [a, b] such that fprime(x)>0, for all x∈(a,b). Then prove that f is an increasing function on (a, b).

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Question

Let f be a function defined on [a, b] such that $f^{p r i m e} (x) > 0$ , for all $x \in (a, b)$ . Then prove that f is an increasing function on (a, b).

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Let f be a function defined on [a, b] such that

f^{p r i m e} (x) > 0

, for all

x \in (a, b)

. Then prove that f is an increasing function on (a, b).

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Question Text

Let f be a function defined on [a, b] such that

f^{p r i m e} (x) > 0

, for all

x \in (a, b)

. Then prove that f is an increasing function on (a, b).