1.1/1 points | Previous AnswersLarCalc11 3.2.004.My Notes
Question Part
Points
Submissions Used
Explain why Rolle's Theorem does not apply to the function even though there
exist a and b such that f(a) = f(b). (Select all that apply.)
f(x) = cot
x
2
,
[π, 5π]
f(a) does not equal f(b) for all possible values of a and b in the interval [π, 5π]. None
of these. f '(a) does not equal f '(b) for any values in the interval [π, 5π]. There are
points on the interval (a, b) where f is not differentiable. There are points on the
interval [a, b] where f is not continuous.
Practice Another Version
2.1/1 points | Previous AnswersLarCalc11 3.2.006.My Notes
Explain why Rolle's Theorem does not apply to the function even though there
exist a and b such that f(a) = f(b). (Select all that apply.)
f '(a) does not equal f '(b) for any values in the interval [-1, 1]. There are points on
the interval [a, b] where f is not continuous. There are points on the interval (a, b)
where f is not differentiable. f(a) does not equal f(b) for all possible values
, of a and b in the interval [-1, 1]. None of these.
3.1/1 points | Previous AnswersLarCalc11 3.2.019.My Notes
Determine whether Rolle's Theorem can be applied to f on the closed interval
[a, b].
(Select all that apply.)
f(x) = 7 sin x, [0, 2π]
Yes, Rolle's Theorem can be applied. No, because f is not continuous on the closed
interval [a, b]. No, because f is not differentiable in the open interval (a, b). No,
because f(a) ≠ f(b).
If Rolle's Theorem can be applied, find all values of c in the open interval
(a, b)
such that
f '(c) = 0.
(Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter
NA.)
c=
$$π2,3π2
Practice Another Version
4.1/1 points | Previous AnswersLarCalc11 3.2.020.My Notes
Question Part
Points
Submissions Used
Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select
all that apply.)
, f(x) = cos x, [π, 3π]
Yes. No, because f is not continuous on the closed interval [a, b]. No, because f is
not differentiable in the open interval (a, b). No, because f(a) ≠ f(b).
If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that
f '(c) = 0.
(Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter
NA.)
c=
$$2π
5.0.5/1 points | Previous AnswersLarCalc11 3.2.021.My Notes
Question Part
Points
Submissions Used
Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select
all that apply.)
f(x) = 4 cos πx, [0, 2]
Yes, Rolle's Theorem can be applied. No, because f is not continuous on the closed
interval [a, b]. No, because f is not differentiable in the open interval (a, b). No,
because f(a) ≠ f(b).
If Rolle's theorem can be applied, find all values of c in the open interval (a, b) such that
f '(c) = 0.
(Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter
NA.)
c=
Question Part
Points
Submissions Used
Explain why Rolle's Theorem does not apply to the function even though there
exist a and b such that f(a) = f(b). (Select all that apply.)
f(x) = cot
x
2
,
[π, 5π]
f(a) does not equal f(b) for all possible values of a and b in the interval [π, 5π]. None
of these. f '(a) does not equal f '(b) for any values in the interval [π, 5π]. There are
points on the interval (a, b) where f is not differentiable. There are points on the
interval [a, b] where f is not continuous.
Practice Another Version
2.1/1 points | Previous AnswersLarCalc11 3.2.006.My Notes
Explain why Rolle's Theorem does not apply to the function even though there
exist a and b such that f(a) = f(b). (Select all that apply.)
f '(a) does not equal f '(b) for any values in the interval [-1, 1]. There are points on
the interval [a, b] where f is not continuous. There are points on the interval (a, b)
where f is not differentiable. f(a) does not equal f(b) for all possible values
, of a and b in the interval [-1, 1]. None of these.
3.1/1 points | Previous AnswersLarCalc11 3.2.019.My Notes
Determine whether Rolle's Theorem can be applied to f on the closed interval
[a, b].
(Select all that apply.)
f(x) = 7 sin x, [0, 2π]
Yes, Rolle's Theorem can be applied. No, because f is not continuous on the closed
interval [a, b]. No, because f is not differentiable in the open interval (a, b). No,
because f(a) ≠ f(b).
If Rolle's Theorem can be applied, find all values of c in the open interval
(a, b)
such that
f '(c) = 0.
(Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter
NA.)
c=
$$π2,3π2
Practice Another Version
4.1/1 points | Previous AnswersLarCalc11 3.2.020.My Notes
Question Part
Points
Submissions Used
Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select
all that apply.)
, f(x) = cos x, [π, 3π]
Yes. No, because f is not continuous on the closed interval [a, b]. No, because f is
not differentiable in the open interval (a, b). No, because f(a) ≠ f(b).
If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that
f '(c) = 0.
(Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter
NA.)
c=
$$2π
5.0.5/1 points | Previous AnswersLarCalc11 3.2.021.My Notes
Question Part
Points
Submissions Used
Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select
all that apply.)
f(x) = 4 cos πx, [0, 2]
Yes, Rolle's Theorem can be applied. No, because f is not continuous on the closed
interval [a, b]. No, because f is not differentiable in the open interval (a, b). No,
because f(a) ≠ f(b).
If Rolle's theorem can be applied, find all values of c in the open interval (a, b) such that
f '(c) = 0.
(Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter
NA.)
c=
