Rolle's theorem is a special case of

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Question

This question was previously asked in

BPSC Assistant Professor Mechanical 2022 Official Paper

Answer 1

Explanation:

Rolle's Theorem:

Let f(x) be defined in [a,b] such that

(i) f(x) is continuous in [a,b]

(ii) f(x) is differentiable in (a,b)

(iii) f(a) = f(b)

then there exists at least one point c ∈ (a,b) such that f'(c) = 0

Lagrange's Mean value theorem:

Let f(x) is a function define on [a ,b] such that,

Then, there exist a real number C ∈ (a , b) such that, According to Lagrange Mean Value Theorem,

f'(c) = \(\frac{{f\left( b \right) ~- ~f\left( a \right)}}{{b ~-~ a}}\)