Why-are-following-statements-wrong-a-There-exists-a-function-with-domain-R-satisfying-f-x-lt-0-x-f-x-gt-0-x-and-f-x-gt-0-x-b-If-f-c-0-then-c-f-c-is-an-inflection-point-

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Question Number 37143 by rahul 19 last updated on 09/Jun/18

$$\mathrm{Why}\mathrm{are}\mathrm{following}\mathrm{statements}\mathrm{wrong}?$$$$\mathrm{a})\mathrm{There}\mathrm{exists}\mathrm{a}\mathrm{function}\mathrm{with}\mathrm{domain}$$$$\mathrm{R}\mathrm{satisfying}\mathrm{f}\left(\mathrm{x}\right)<0\mathrm{\forall }\mathrm{x},{\mathrm{f}}^{\prime }\left(\mathrm{x}\right)>0\mathrm{\forall }\mathrm{x}\mathrm{and}$$$${\mathrm{f}}^{″}\left(\mathrm{x}\right)>0\mathrm{\forall }\mathrm{x}.$$$$$$$$\mathrm{b})\mathrm{If}{\mathrm{f}}^{″}\left(\mathrm{c}\right)=0\mathrm{then}(\mathrm{c},\mathrm{f}\left(\mathrm{c}\right))\mathrm{is}\mathrm{an}\mathrm{inflection}$$$$\mathrm{point}.$$

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