We introduce the intermediate value theorem for continuous functions and see how to apply the intermediate value theorem to find the roots of an equation on an interval. The intermediate value theorem states that if f is a continuous function on a closed interval [a,b] then it must take on every value between f(a) and f(b) at some point in the interval. So if N is a number between f(a) and f(b) then there exists c in (a,b) such that f(c) = N. #calculus #apcalculus Join Wrath of Math to get exclusive videos, lecture notes, and more: Continuous Functions Explained: (coming soon) The Extreme Value Theorem: Using Intermediate Value Theorem to Find Roots: Calculus 1 Exercises playlist: Calculus 1 playlist: Get the textbook for this course! ★DONATE★ ◆ Support Wrath of Math on Patreon: ◆ Donate on PayPal: Follow Wrath of Math on... ● Instagram: ● TikTok: @wrathofmathedu ● X: ● Facebook: