Question

significance of rolles theorem​

Answer 1

Answer:

Rolle's theorem, in analysis, special case of the mean-value theorem of differential calculus. 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.

Answer 2

Answer:

It essentially states that any real-valued differentiable function that attains equal values at two distinct points must have at least one stationary point somewhere between them—that is, a point where the first derivative (the slope of the tangent line to the graph of the function) is zero.