f'(c) = |
Problem :
1)
f (x) = x
^{2} - 4x
on
[2, 4]
f'(c) | = | = 2 | |
2c - 4 | = | 2 | |
c | = | 3 |
Problem :
2)
f (x) = sin(x) + cos(x)
on
[0, 4Π]
f'(c) = = 0 | |||
cos(x) - sin(x) = 0 | |||
x = ,,, or |
Problem :
3)
f (x) =
on
[1, 2]
f'(c) | = | ||
= - | |||
- | = - | ||
c | = ± |
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]
.