We introduce the Extreme Value Theorem, which states that if f is a continuous function on a closed interval [a,b], then f takes on a maximum f(c) and a minimum f(d) at points c and d in the interval [a,b]. We also discuss critical points/critical numbers and their importance to finding extreme values. We then look at several examples of continuous and discontinuous functions where the EVT does and doesn't apply. We finish with a basic set of Extreme Value Theorem problems. Find Absolute Extrema on Closed Interval: Calculus 1 Exercises playlist: Calculus 1 playlist: ◉Textbooks I Like◉ Graph Theory: Real Analysis: Proofs and Set Theory: (available for free online) Statistics: Abstract Algebra: Discrete Math: Number Theory: ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: ◆ Donate on PayPal: Thanks to Petar, dric, Rolf Waefler, Robert Rennie, Barbara Sharrock, Joshua Gray, Karl Kristiansen, Katy, Mohamad Nossier, and Shadow Master for their generous support on Patreon! Follow Wrath of Math on... ● Instagram: ● Facebook: ● Twitter: My Math Rap channel: