IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

ankitagg

assertion and reasoning::

statement 1- if f(x)= ${e}^{(x-1)(x-3)}$ ,then rolle's theoram applies for f(x) in [1,3]

statemaent 2- lagrange's mean value theoram is applicable to f(x)= ${e}^{(x-1)(x-3)}$ in any inteval.

pranay_robot

its not continious in the closed interval [ 1 3] but satisfies f(a) = f(b) hence rolles theroem not applicable - state ment 1

allamraju

I think the function is continuous in [1,3] and derivable in (1,3) and f(1)=f(3).So,Rolle's theorem holds.Robot,Can u explain why it isn't continuous in [1,3].

Similarly,LMVT holds for f(x) in any interval as it is continuous and derivable on R.So,the answer is that both are true,but R is not correct explanation of A.

[edited]

me

f(x) is continuous [1,3] and derivable in (1,3) and f(1)=f(3).So,Rolle's theorem holds.

at the same time, lagrange's mean value theoram is applicable to f(x) in any inteval.

but statement 2 is in no case proper explanation for statement 1

pranay_robot

iam sorry ,small mistake in calculation continuity holds ...

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I think the function is continuous in [1,3] and derivable in (1,3) and f(1)=f(3).So,Rolle's theorem holds.Robot,Can u explain why it isn't continuous in [1,3].

Similarly,LMVT holds for f(x) in any interval as it is continuous and derivable on R.So,the answer is that both are true,but R is not correct explanation of A.

[edited]