Topmusicanswers
Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.
- What is Rolle's theorem Class 12?
- What are the three conditions of Rolle's theorem?
- Is Rolle's theorem the same as MVT?
What is Rolle's theorem Class 12?
Rolle's theorem essentially states that any real-valued differential function that attains equal values at two distinct points on it, must have at least one stationary point somewhere in between them, that is a point where the first derivative (the slope of the tangent line to the graph of a function) is zero.
What are the three conditions of Rolle's theorem?
All three conditions of Rolle's theorem are important for the theorem to be true: Condition 1: f(x) is continuous on the closed interval [a,b]; Condition 2: f(x) is differentiable on the open interval (a,b); Condition 3: There exists point x = c, f'(c) = 0, for c belongs to ]a, b].
Is Rolle's theorem the same as MVT?
Rolle's theorem is clearly a particular case of the MVT in which f satisfies an additional condition, f(a) = f(b).) ... This Wolfram Demonstration, Rolle's Theorem, shows an item of the same or similar topic, but is different from the original Java applet, named 'MVT'.
