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
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]
