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$f(x)=x_{3}?4.5x_{2}?12x+3$ a) Determine the intervals on which $f$ is concave up and concave down. $f$ is concave up on: $f$ is concave down on: b) Based on your answer to part (a), determine the inflection points of $f$. Each point should be entered as an ordered pair (that is, in the form $(x,y)$ ). (Separate multiple answers by commas.) c) Find the critical numbers of $f$ and use the Second Derivative Test, when possible, to determine the relative extrema. List only the $x$-coordinates. Relative maxima at: (Separate multiple answers by commas.) Relative minima at: (Separate multiple answers by commas.) d) Find the $x$-value(s) where $f_{?}(x)$ has a relative maximum or minimum. $f_{?}$ has relative maxima at: (Separate multiple answers by commas.) $f_{?}$ has relative minima at: (Separate multiple answers by commas.)

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