    Question

# On which of the following functions can we apply LMVT in the interval [-2,2] ?

A

Y=|x|

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B

y = ex

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C

y=x3

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D

y=[x]

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E

y=cosx

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Solution

## The correct options are B y = ex C y=x3 E y=cosx LMVT says that if y = f(x) be a given function which is ; 1.Continuous in [a,b] 2.Differentiable in (a,b) Then, f'(c) = f(b)−f(a)b−a for some c ϵ (a , b) So, to apply LMVT the function must be continuous and differentiable in the given interval A.We know that |x| has a sharp edge at x = 0 making it non-differentiable at x = 0. So we can’t apply LMVT on |x| B. y = exis continuous and differentiable in its domain. So we can apply LMVT on this function C. x3 This is also one of the answers D. Y= =[x]. As we know, [x] is discontinuous at all the integers. So we can’t apply LMVT E. Y= = cosx is continuous and differentiable at all the points. Hence we can apply LMVT on cosx So the answers are B, C and E  Suggest Corrections  0      Similar questions
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