Identifying Optima

Optimization · Axiom Academy

Learn to find and classify local and global extrema using calculus techniques Excellent work! You've successfully identified all local and global extrema. Here's what we learned: Critical Points: Found by setting the first derivative equal to zero. For this problem, x = 1 and x = 3 were our critical points. Second Derivative Test: Determines if critical points are local minima (f''(x) > 0) or local maxima (f''(x) x = 1 and a local minimum at x = 3 . Global Extrema: Must evaluate the function at critical points AND endpoints of the interval. The global maximum was f(1) = 5 and the global minimum was f(3) = 1 . Boundary Points Matter: Don't forget to check endpoints! In this case, f(0) = 1 and f(5) = 21 were both evaluated to ensure we found the true global extrema. This systematic approach works for any optimization problem: find critical points, classify them, check boundaries, and compare values. Master this process and you'll be ready to tackle real-world optimization challenges!

This is the written version of the interactive lesson above. See the full Optimization course.