Grade 11Integral Calculus

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

KOMATI UMESH

12 Years agoGrade 11

1 Answer

bharat bajaj

Approved Tutor Answer12 Years ago

Langrange Mean Therorem : Let $f:[a,b]\rightarrow\mathbb{R}$ be acontinuous function,differentiableon theOpen interval (page does not exist) $(a,b)$ . Then there exists some $c\in (a,b)$ such that $f'(c)=\frac{f(b)-f(a)}{b-a}$ .
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 that $f'(c)=\frac{f(b)-f(a)}{b-a}$ .

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Bharat Bajaj

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IIT Delhi