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GO Classes Test Series 2023 | Calculus | Test 1 | Question: 10

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Consider the following statements:

  1. $f(x)$ is continuous on $[a, b]$
  2. $f(x)$ is differentiable on $(a, b)$
  3. $f(a)=f(b)$

Which of the above statements are required in order to guarantee a $c \in(a, b)$ such that $f^{\prime}(c)(b-a)=f(b)-f(a) ?$

  1. I only
  2. I and II only
  3. I, II, and III
  4. I and III only
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