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I am a bit confused over something that should be relatively easy to research , however, I am having a hard time finding a direct answer to my question.
When finding the extrema of a function , we find at what points the first derivative is 0 or undefined .. with the stipulation , if I am not mistaken , that the function itself IS defined at those values(continuous but not necessarily differentiable at those points) .. if they are not , then they will not be critical numbers per the definition . .
when finding concavity / points of inflection .. i am assuming the continuity requirement for the original function with respect to the critical numbers of the second derivative is dropped . am i right ? ..also , can I automatically assume if there are discontinuties in the original function , those will serve as critical numbers for sake of determining concavity ?
i am getting conflicting information but my intuition tells me this has to be so . just by looking at a couple graphs.concavity changes between vertical asymptotes. but i just wanted to make sure .. my book sucks. =D
When finding the extrema of a function , we find at what points the first derivative is 0 or undefined .. with the stipulation , if I am not mistaken , that the function itself IS defined at those values(continuous but not necessarily differentiable at those points) .. if they are not , then they will not be critical numbers per the definition . .
when finding concavity / points of inflection .. i am assuming the continuity requirement for the original function with respect to the critical numbers of the second derivative is dropped . am i right ? ..also , can I automatically assume if there are discontinuties in the original function , those will serve as critical numbers for sake of determining concavity ?
i am getting conflicting information but my intuition tells me this has to be so . just by looking at a couple graphs.concavity changes between vertical asymptotes. but i just wanted to make sure .. my book sucks. =D