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what is the graphical interpretation of the fact that a f''(x) >0 for a range of values of x? I am confused if it would give a number of minimas or something else. Really confused :|

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The second derivative determines whether a function is convex (for $f''>0$) or concave (for $f''<0$). (And $f''=0$ may be the inflection point, if changes sign there.)

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