I need to find the intervals on which the following equations have zeroes, extrema, points of inflection and intervals increasing or decreasing, as well as concave up or down. I need to show these on a graph but is there a better way to present the data (before graphing) instead of just x=1 and sub into equation, then x=2, and so on? Thanks in advance

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Equation 1) \[f(x) =x^2 +\frac{ 1 }{ x }\]
Equation 2) \[h(x) =x^3-9x^2+27x\]

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