Rolle's Theorem Explained (with proof) | Calculus 1
We introduce Rolle's theorem which we will later use in a proof of the Mean Value theorem. Rolle's theorem states that if a function is continuous on [a,b] and differentiable on (a,b), and f(a)=f(b), then there exists a point c in (a,b) so that f'(c)=0, that is - a place where the derivative is 0. We'll prove Rolle's theorem and go through two examples of using Rolle's theorem. In the first example we will find two x-intercepts of our function then use Rolle's theorem, and in the other example we will use Rolle's theorem to prove a cubic has only one root. #calculus1 #apcalculus
Join Wrath of Math to get exclusive videos, lecture notes, and more:
/ @wrathofmath
Calculus 1 Exercises playlist: • Calculus 1 Exercises
Calculus 1 playlist: • Calculus 1
Get the textbook for this course! https://amzn.to/3PieD1M
0:00 Intro
0:15 Rolle's Theorem
1:00 Rolle's Theorem Visualized
2:27 Proof of Rolle's Theorem
5:33 Example 1 of using Rolle's Theorem
7:30 Example 2 of using Rolle's Theorem
10:25 Conclusion
★DONATE★
◆ Support Wrath of Math on Patreon: / wrathofmathlessons
◆ Donate on PayPal: https://www.paypal.me/wrathofmath
Outro music by Ben Watts and is available for channel members.
Follow Wrath of Math on...
● Instagram: / wrathofmathedu
● TikTok: / wrathofmathedu
● X: https://x.com/wrathofmathedu
● Facebook: / wrathofmath
Watch video Rolle's Theorem Explained (with proof) | Calculus 1 online without registration, duration hours minute second in high quality. This video was added by user Wrath of Math 23 August 2024, don't forget to share it with your friends and acquaintances, it has been viewed on our site 551 once and liked it 37 people.