6ed8c1…: “Left of the famous quadrilateral”

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Worked Out Examples Problem Videos

The following video may be helpful when trying to solve this example. Note that you may skip to the end of the video to get completion credit for this page if you don’t need to watch it.

Practice Problems: Curve Sketching

Calculate what is needed to graph the function: $\sage {p1f2}$

Sum of the $x$ values that are domain restrictions: (If there are no restrictions, enter DNE) $\answer {DNE}$
Sum of the $x$ values that are local maximums (If there are none, enter DNE): $\answer {\sage {p1xmaxSum}}$
Sum of the $y$ values that are local maximums (If there are none, enter DNE): $\answer {\sage {p1ymaxSum}}$
Sum of the $x$ values that are local minimums (If there are none, enter DNE): $\answer {\sage {p1xminSum}}$
Sum of the $y$ values that are local minimums (If there are none, enter DNE): $\answer {\sage {p1yminSum}}$
Sum of the $x$ values that are points of inflection (If there are none, enter DNE): $\answer {\sage {p1xpoiSum}}$
Sum of the $y$ values that are points of inflection (If there are none, enter DNE): $\answer {\sage {p1ypoiSum}}$
Sum of the $x$ values that are zeros (If there are none, enter DNE): $\answer {\sage {p1xzeroSum}}$
The $y$ -intercept is: $(\answer {0},\answer {\sage {p1yInt}})$
The right horizontal asymptote is (if there isn’t one, enter DNE): $\answer {DNE}$
The left horizontal asymptote is (if there isn’t one, enter DNE): $\answer {DNE}$

The original function should be factorable by grouping, and the derivatives should also be able to be factored using standard techniques (without anything like the quadratic formula), but the tradeoff for making this possible is that some of the y-value summations might be annoyingly large.