Théorème de Rolle - La Dérivation - 2 Bac SM - [Exercice 7]

In this video, I'll work through an exercise applying Rolle's Theorem. This video is intended for second-year high school students specializing in science and technology. 💡Remember, it's important to try the exercise yourself before watching the solution. ▬▬▬▬▬▬▬ Exercise ▬▬▬▬▬▬▬ Exercise: (Al Moufid) Let f be a continuous function on [a,b] and twice differentiable on ]a,b[ such that f(a) = f(b) = 0 and f''(x) ≠ 0 for all x ∈ ]a,b[. Prove by contradiction that f(x) ≠ 0 for all x ∈ ]a,b[. 00:29 Statement of the exercise 01:02 Statement of the Mean Value Theorem 01:28 Question 1) 12:32 Question 2) ▬▬▬▬▬▬▬ SUBJECTS RELATED ▬▬▬▬▬▬▬ 2nd year Baccalaureate in Mathematical Sciences 2nd year Baccalaureate in Science and Technology (SM) Baccalaureate in Biology and Geography (BIOF) 2nd year Baccalaureate in Mathematical Sciences Final year National exam ▬▬▬▬▬▬▬ SUBSCRIBE ▬▬▬▬▬▬▬ 💡👉 Subscribe Here:    / @mathphys   ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 🔔 Please click the LIKE button if you enjoy our content, leave a comment, and subscribe to our YouTube channel to receive our new videos. 👉Write your questions in the comments section if you didn't understand something! 😀 💡Don't forget to SHARE with your friends! Please!! 💪💪🔥🔥 ▬▬▬▬▬▬▬ SOCIAL MEDIA ▬▬▬▬▬▬▬   / math-phys-112225370317476     / mathphys5   ▬▬▬▬▬▬▬ SIMILAR VIDEOS ▬▬▬▬▬▬▬ Rolle's Theorem - Differentiation - 2nd Year Baccalaureate (Mathematics and Physics) - [Exercise 7]:    • Théorème de Rolle - La Dérivation - 2 Bac ...   Mean Value Theorem - TAF - 2 Bac SM - [Exercise 6]:    • Théorème des Accroissements Finis - TAF - ...   Differentiability of a Function - Differentiability on an Interval - 2 Bac SM - [Exercise 2]:    • La Dérivabilité d'une Fonction - Dérivabil...   Differentiability - Differentiation - Derivative - 2 Bac SM - [Exercise 1]:    • Dérivabilité - Dérivation - Nombre Dérivé ...   Rolle's Theorem - Differentiation - 2 Bac SM - [Exercise 5]:    • Théorème de Rolle - Dérivation - 2 Bac SM ...   Rolle's Theorem - Differentiation - 2 Bac SM - [Exercise 3]:    • Théorème de Rolle - La Dérivation - 2 Bac ...   Finite Increment Theorem - FIT - nth Root - 2nd Year Baccalaureate Science and Technology (SM) - [Exercise 4]:    • Théorème des Accroissements Finis - TAF - ...   Finite Increment Theorem - FIT - Inequality of Finite Increments - FIT - 2nd Year Baccalaureate Science and Technology (SM):    • THÉORÈME DES ACCROISSEMENTS FINIS TAF - IN...   Finite Increment Theorem - FIT - 2nd Year Baccalaureate Science and Technology (SM) - [EXERCISE 2]:    • THÉORÈME DES ACCROISSEMENTS FINIS TAF - 2 ...   ▬▬▬▬▬▬▬▬▬ Video Summary ▬▬▬▬▬▬▬▬▬ • In In mathematics, and more specifically in analysis, Rolle's theorem, named after Michel Rolle, is a fundamental result concerning the derivative of a real function of a real variable. It states that if a differentiable function takes the same value at two points, then its derivative is zero at least once between those two points. • This means that there exists a point where the tangent to the curve y = f(x) is horizontal. • To say that there exists at least one point where the derivative of f is zero means that it is not unique; there can be several. • This theorem is used in the proof of the Mean Value Theorem (of which it is a special case). • This theorem is used to find simple expressions for calculating the limit of a function. • You can also check out the other videos in this playlist to see more exercises on "Rolle's Theorem" and "Mean Value Theorem." "Finished" with all the tips and methods for solving them. YouTube has become a real math site (math fr) for science and engineering students, offering math courses and online math resources. In this video, we'll focus on the math course on Rolle's Theorem and the Theorem of the Fundamental Principle (TAF). ▬▬▬▬▬▬▬▬ KEYWORDS ▬▬▬▬▬▬▬▬ #Rolle_Theorem #Math #Exercise