Question: Showing all work to be written, for the function \(F\left( x \right)=\frac{{{x}^{3}}+32}{{{x}^{2}}}=x+\frac{32}{{{x}^{2}}}\)

1. Find f '(x)
2. Find the critical numbers of f.
3. Using a tabular sign analysis on f', identify the intervals where the function f is increasing and where f is decreasing.
4. Using the First Derivative Test, find the points which are the relative minimum and relative maximum of function f.
5. Find f"(x)
6. Find the critical numbers of f'
7. Using a tabular sign analysis on f", identify the intervals where f is concave upward and where f is concave downward.
8. Find the point(s) of inflection.
9. Accurately sketch and label the graph of the function f.

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Deliverable: Word Document