This question is based on Section $4\mathrm{.}5$ and Section $4\mathrm{.}6.$ Leave answers as exact values.

Consider the function

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f$($x$)=$x$^\{4\}-6$ x$^\{3\}$

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PART A$.[6$ MARKS$].$ Determine the intervals where the graph increases and decreases by using the first derivative. Identify any minimum and maximum values. Some sort of sign chart or sign analysis is required.

PART B$.[5$ MARKS$].$ Determine the intervals where the graph is concave up and concave down by using the second derivative. Identify any inflection points. Some sort of sign chart or sign analysis is required.

PART C$.[1$ MARK$].$ Graph the function on Desmos. Identify the minimum and maximum points, and any inflection points.