7b4f7e…: “By the gray 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: Local Extrema

For the following problems, let $f(x) = \sage {p1f1disp}$ .

1 : How many local minimums does $f(x)$ have? $\answer {\sage {p1ansMin}}$ .

We could actually answer this with precalc knowledge, but since we will need to actually find the values anyway it’s best to do this with calculus. To do that, remember you will want to take the derivative and then factor it to make a sign chart. Wherever the sign chart changes from negative to positive will be a minimum, and wherever it changes from positive to negative will be a maximum!

1.1 : What is the sum of the $x$ value(s) that have local minimums? $\answer {\sage {p1ansMinxSum}}$

Since this just wants the sum of the $x$ value(s), you just want to add up the $x$ values that had local minimums from your sign chart in the previous step.

1.2 : What is the sum of the value(s) of the local minimums? $\answer {\sage {p1ansMinySum}}$

Remember that the value(s) of the local minimums is the actual $y$ values, so you need to plug in the individual $x$ values you found in the original step on your sign chart, into the function $\sage {p1f1disp}$ and add up the $y$ values that you get!

2 : How many local maximums does $f(x)$ have? $\answer {\sage {p1ansMax}}$ .

2.1 : What is the sum of the $x$ value(s) that have local maximums? $\answer {\sage {p1ansMaxxSum}}$

Since this just wants the sum of the $x$ value(s), you just want to add up the $x$ values that had local maximums from your sign chart in the previous step.

2.2 : What is the sum of the value(s) of the local maximums? $\answer {\sage {p1ansMaxySum}}$

Remember that the value(s) of the local maximums is the actual $y$ values, so you need to plug in the individual $x$ values you found in the original step on your sign chart, into the function $\sage {p1f1disp}$ and add up the $y$ values that you get!