19f8cb…: “As regards the happy city”

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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

1 : Calculate what is needed to graph the function: $\sage {p4f1}$ .

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): $\answer {\sage {p4xmaxSum}}$
Sum of the $y$ values that are local maximums (If there are none, enter DNE): $\answer {\sage {p4ymaxSum}}$
Sum of the $x$ values that are local minimums (If there are none, enter DNE): $\answer {\sage {p4xminSum}}$
Sum of the $y$ values that are local minimums (If there are none, enter DNE): $\answer {\sage {p4yminSum}}$
Sum of the $x$ values that are points of inflection (If there are none, enter DNE): $\answer {\sage {p4xpoiSum}}$
Sum of the $y$ values that are points of inflection (If there are none, enter DNE): $\answer {\sage {p4ypoiSum}}$
Sum of the $x$ values that are zeros (If there are none, enter DNE): $\answer {\sage {p4xzeroSum}}$
The $y$ -intercept is: $(\answer {0},\answer {\sage {p4yInt}})$
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): $\answer {DNE}$

Remember that, in order for a limit to exist, both the left and right limits must exist and be equal.