# Calculus AB: Applications of the Derivative

### 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 : 1) f (x) = x 2 - 4x on [2, 4]

Problem : 2) f (x) = sin(x) + cos(x) on [0, 4Π]

Problem : 3) f (x) = on [1, 2]

Problem : 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?

Problem : Find the number c that satisfies Rolle's theorem for f (x) = sin(x) on the interval [0, Π] .

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