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C$($x$)=$x$^\{\backslash$wedge$\}3-5$ x$^\{\backslash$wedge$\}2+6$ x

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d$.$ Partition the derivative and identify the intervals where the derivative is positive or negative. Explain what this implies for the behavior of the function.

e$.$ Partition the second derivative and identify the intervals where the second derivative is positive or negative. Explain what this implies about the concavity of the function.

f$.$ Sketch the graph of the function, including zeros, extrema, and inflection points. You may use a computer application for the graph.