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Discuss the Application and conclusion of Lagranges`s Mean Value Theorem on the function f(x) = |x| on interval [-1, 1].

Discuss the Application and conclusion of Lagranges`s Mean Value Theorem on the function f(x) = |x| on
interval [-1, 1].

Grade:11

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
8 years ago
Langrange Mean Therorem : Letf:[a,b]\rightarrow\mathbb{R}be acontinuous function,differentiableon theOpen interval (page does not exist)(a,b). Then there exists somec\in (a,b)such thatf'(c)=\frac{f(b)-f(a)}{b-a}.
The function is continuous but not differentiable in the interval (-1,1) at x=0. Hence, lagrange's mean value therorem cannot be applied to this function. Hence, there doesnt exists any c such thatf'(c)=\frac{f(b)-f(a)}{b-a}.
Thanks & Regards
Bharat Bajaj
askIITians Faculty
IIT Delhi

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