1965 AHSME Problems/Problem 34
For the smallest value of is:
To begin, lets denote the equation, as . Let's notice that:
After this simplification, we may notice that we may use calculus, or the AM-GM inequality to finish this problem because , which implies that both are greater than zero. Continuing with AM-GM:
Solution 2 (Calculus)
Take the derivative of f(x) and f'(x) using the quotient rule.