- #1
bomba923
- 763
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*Let [itex] f\left( x \right) [/itex] be a twice-differentiable function for which
[tex] \; \mathop {\lim }\limits_{x \to 0^ - } f\left( x \right) = \infty [/tex]
Then, is it true that
[tex] \mathop {\lim }\limits_{x \to 0^ - } f\,{''}\left( x \right) > 0\;? [/tex]
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Or a little differently,
*Let [itex] f\left( x \right) [/itex] be a twice-differentiable function for which
[tex]\mathop {\lim }\limits_{x \to 0^ - } f\left( x \right) = \infty \;{\text{and }}\forall x < 0,f\,'\left( x \right) > 0 [/tex]
Then, is it true that
[tex] \mathop {\lim }\limits_{x \to 0^ - } f\,{''}\left( x \right) > 0\;? [/tex]
Just curious|
[tex] \; \mathop {\lim }\limits_{x \to 0^ - } f\left( x \right) = \infty [/tex]
Then, is it true that
[tex] \mathop {\lim }\limits_{x \to 0^ - } f\,{''}\left( x \right) > 0\;? [/tex]
----------------------------------------------
Or a little differently,
*Let [itex] f\left( x \right) [/itex] be a twice-differentiable function for which
[tex]\mathop {\lim }\limits_{x \to 0^ - } f\left( x \right) = \infty \;{\text{and }}\forall x < 0,f\,'\left( x \right) > 0 [/tex]
Then, is it true that
[tex] \mathop {\lim }\limits_{x \to 0^ - } f\,{''}\left( x \right) > 0\;? [/tex]
Just curious|
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