Question 1208035
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The student said in a thank-you note to me:

"This is probably your best reply ever."

So I assume s/he is a calculus student.  It seemed likely to me because

teachers do not assign Math Olympiad type problems to students.  But finding

the range makes this a very good maxima and minima problem.  Only a calculus 

teacher would assign this.  It requires the factoring of a -1/2 power out of 

a 1/2 power, leaving a power of 1, which is a necessary technique in 

taking derivatives of expressions involving roots. That's because the
 
product and quotient rules for differentiation often involve exponents which 

differ by one, whenever the power rule is used, which is always the case in

expressions with roots. 

Edwin</pre>