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  Home : Math & Science : Math Study Guides : Calculus AB : The Derivative : Problems for "The Mean Value Theorem"
Applications of the Derivative (AB)
  
 
Problems for "The Mean Value Theorem"

In problems 1-3, for each of the following functions f defined on [a, b] find the c on [a, b] such that

f'(c) =
   

Problem 4.1: 1) f (x) = x2 - 4x on [2, 4]
[Solution]
Problem 4.2: 2) f (x) = sin(x) + cos(x) on [0, 4π]
[Solution]
Problem 4.3: 3) f (x) =
on [1, 2]
[Solution]
Problem 4.4: 4) On the interval [-5,5], there is no point at which the derivative of f (x) =|x| is equal to zero, even though f (- 5) = f (5). Is this a contradiction of Rolle's theorem?
[Solution]
Problem 4.5: Find the number c that satisfies Rolle's theorem for f (x) = sin(x) on the interval [0, π].
[Solution]
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