Let the function, be continuous on and differentiable on . If and for all then for all such functions lies in the interval :
Option: 1
Option: 2
Option: 3
Option: 4
Lagrange’s Mean Value Theorem -
Lagrange’s Mean Value Theorem
Rolle’s theorem is a special case of the Mean Value Theorem. In Rolle’s theorem, we consider differentiable functions f defined on a closed interval [a, b] with f(a) = f(b) . The Mean Value Theorem generalized Rolle’s theorem by considering functions that do not necessarily have equal value at the endpoints.
Statement
Let f (x) be a function defined on [a, b] such that
it is continuous on [a, b],
it is differentiable on (a, b).
Then there exists a real number c (a, b) such that
-
Directly use
we get
Correct Option (2)
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