Run-time analysis of distributed network decomposition algorithm
Calculus: any local minimum of the function $f(x)$ must be a point $x$ that satisfies $f'(x)=0$, where $f'(x)$ is the first derivative of $f(x)$.  So, take the derivative, set it to zero, and find all solutions.  Each solution is a candidate for the minimum.  You then need to check each candidate to see which makes $f(x)$ smallest.  You'll also need to check the "endpoints", e.g., the smallest and largest possible value for $x$ need to be added as candidates.

You can do the same for functions of two variables, and for asymptotics.