Identify the function and its domain
Determine whether the function is continuous and differentiable on the domain
Find critical points by solving where the first derivative equals zero or does not exist
Check endpoints of the domain if they exist
Evaluate the function at all critical points and endpoints
Compare the values to find the smallest one
If using a graph, locate the lowest point on the curve within the domain
If the function is convex, verify the minimum by checking that the second derivative is nonnegative at the critical point
For constrained problems, use substitution or optimization methods such as Lagrange multipliers
Confirm the minimum is global if required by the problem