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A function f: R->R is such that f^(...

A function `f: R->R` is such that `f^(prime)(x)=0` at `x=0\ a n d\ x=2` `f^(prime)(x)<0\ ` in `0 lt x<<2\ a="" n="" d\="" x="">>2` `f^(prime)(x)>0\ ` for `x<0` Which of the following does not hold good? The graph of `f` has a local maximum point at `x=2` The graph of `f` has a point of inflection at `x=2` The graph of `f` has a local minimum point at `x=0` The graph of `f` has a local minimum point at `x=2`

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