PLEASE HELP!! i dont know how to fill in these blanks! Optimization $3$

Enter all your answers as exact numbers in this question $G,$ and bike the rest of the way. If your canoe speed is $4$ times slower than your bike speed, what is the quickest path from your cabin to your friend's cabin?

From the question, we know that the distance from your cabin to point $S$ in km is $$ and the total distance from your friend's cabin to point $S$ in km is $$ so if we let $x$ represent unknown the distance between point $S$ and $C$ in $km,$ then we can express the distance that you ride your bike in $km$ in terms of $x$ as $q,$ We can also express the distance that you canoe in km in terms of $x$ as

Your third and fourth answers in the line above should be in terms of $x$

Now, we will use $B$ to represent the bike speed, which we assume is known

So$,$ the total time, $T,$ that it takes you to get from your cabin to your friend's cabin can be written as a function of $x,$ which would be $T(x)=q,4$B

B$()$

$$

Marks for this submission $1\mathrm{.}00/1\mathrm{.}00.$ Marks for this submission $1\mathrm{.}00/1\mathrm{.}00.$

In order to find the quickest path from your cabin to your friend's cabin, we want to find the $($No answer given$)$ :

$$ of the function $T$

Note that the domain we are considering is $$

$1$

$\backslash$table$[[,],[$Marks for this submission: $1\mathrm{.}00/1\mathrm{.}00.$ Marks for this submission: $1\mathrm{.}00/1\mathrm{.}00.,]]$

So$,$ taking the derivative of $T(x)$ gives us $($

Notice that $T^{\text{'}}(x)=B()$ defined for all real values of $x$

$$

Marks for this submission $1\mathrm{.}00/1\mathrm{.}00$

Also note that $T^{\text{'}}(x)=0$ when $x=$

So$,$ we have $$ critical point in our domain, $x=$

So we will compare the values $T()=B),$ and $$ en note thalthe of these occurs when $x=$

So$,$ for the quickest path from your cabin to your friend's cabin, you should canoe $(0{)}^2,$ then bike for m