Question 1208041
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Answer: <font color=red>1900 mph</font>



Explanation


Apply the derivative with respect to x to go from 
C(x) = 100 + (x/100) + (36000/x)
to
C ' (x) = 0.01 - 36000x^(-2)
I skipped steps and will leave the scratch work for the student to do. 
This solution is basically an outline of sorts.


Set C ' (x) equal to zero and solve for x.
We do this because the local min occurs when the tangent line is 0 (i.e. when the tangent is horizontal).
I'll let the student do the 1st derivative test or 2nd derivative test to confirm that a local min exists on the interval x > 0.


If you were to solve 
0.01 - 36000x^(-2) = 0
then you should get roughly
x = 1897.366596 when considering x > 0 only.
I have confirmed this with GeoGebra. Desmos is another good choice. 
If you are familiar with a TI83 or similar, then you can use that as well. There are many options to pick from.


The last step is to round 1897.366596 to the nearest multiple of 50 to get the <font color=red>answer 1900 mph</font>.
Unfortunately I don't know much about aviation to know if 1900 mph is a realistic ground speed or not. It seems a bit large.



Side note: for students not familiar with calculus just yet, you'll need to rely solely on graphing calculator technology.
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