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Question

Rolle’s Theorem is not applicable for?

  1. f left parenthesis x right parenthesis equals x to the power of 1 divided by 3 end exponent text  on  end text left square bracket negative 1 comma 1 right square bracket
  2. f left parenthesis x right parenthesis equals vertical line x vertical line text  on  end text left square bracket 1 comma 2 right square bracket
  3. f left parenthesis x right parenthesis equals tan to the power of negative 1 end exponent invisible function application x text  on  end text left square bracket 0 comma 1 right square bracket
  4. f left parenthesis x right parenthesis equals x plus 1 over x text  on  end text open square brackets 1 half comma 3 close square brackets

hintHint:

Rolle's Theorem is not applicable for the function which is not differentiable in the open interval.
Rolle's theorem is not applicable if the value of the function is not same at the end point.

The correct answer is: f left parenthesis x right parenthesis equals x to the power of 1 divided by 3 end exponent text  on  end text left square bracket negative 1 comma 1 right square bracket


    Step1: Criteria for the applicability of Rolle's theorem
    Rolle's Theorem is not applicable for the function which is not differentiable in the open interval.
    Rolle's theorem is not applicable if the value of the function is not same at the end point.
    Step2: Checking if Rolle's theorem is applicable or not.
    Since the value of the function f left parenthesis x right parenthesis equals x to the power of 1 divided by 3 end exponent text  on  end text left square bracket negative 1 comma 1 right square bracket at end points
    f left parenthesis negative 1 right parenthesis equals negative 1 and f left parenthesis 1 right parenthesis equals 1 is not same then Rolle's theorem is not applicable on this this function.

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