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According to the mean value theorem  then

  1. a < xt ≤ b
  2. a ≤ xt < b
  3. a < xt < b
  4. a ≤ xt ≤ b

Answer (Detailed Solution Below)

Option 3 : a < xt < b
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Detailed Solution

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Concept:

Mean Value Theorem: Let f  : [a, b] → R be a continuous function on [a, b] and differentiable on (a, b). Then there exists some c in (a, b) such that

f'(c) =  

Explanation:

Given that

According to the mean value theorem, f'(x) will be defined for some value a < xt < b, where f(x) is differentiable.

Hence, correct answer is a < xt < b.

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