Question

rolles theorem of class 12​

Answer 1

Step-by-step explanation:

Rolle’s Theorem:

A special case of Lagrange’s mean value theorem is Rolle ’s Theorem which states that:

If a function f is defined in the closed interval [a,b] in such a way that it satisfies the following conditions.

i) The function f is continuous on the closed interval [a, b]

ii)The function f is differentiable on the open interval (a, b)

iii) Now if f (a) = f (b) , then there exists at least one value of x, let us assume this value to be c, whereas lies between a and b i.e. (a < c < b ) in such a way that f‘(c) = 0 .

Precisely, if a function is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) then there exists a point x = c in (a, b) such that f'(c) = 0