[Summary] Rolle's Theorem

[Summary] Rolle's Theorem

Rolle's Theorem which is a special case of the mean-value theorem states that:

if a function " f " is 

  1. Continuous on the closed interval [ab
  2. Differentiable on the open interval ]a, b
  3. f(a) = f(b

then, there is at least one value ]a, b[ that:

f′(c) = 0 

How can we find the value of  "c"?

  1. We make sure that the function " f " satisfies the conditions of Rolle's theorem
  2. We find  f′(x) (The derivative with respect to "x")
  3. We put  f′(c) (We replace the "x" in the derivative with "c")
  4. We put  f′(c) = 0
  5. Finally, we find the value of "c"
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