Question
In: Math
1) A) Determine whether Rolle's Theorem can be applied to f on the closed interval [a,...
1)
A) Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.)
f(x) = (x − 1)(x − 2)(x − 8), [1, 8]
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).
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 =
2)
A) Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = x2/3 − 2, [−8, 8]
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).
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 =
Solutions
milcah answered 2 years agoRelated Solutions
1. Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]....
1.
Determine whether Rolle's Theorem can be applied to
f
on the closed interval
[a, b].
(Select all that apply.)
f(x)
=
x2− 4x
− 5
x + 5
, [−1,
5]
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)...
Determine whether Rolle's Theorem applies to the following function on the given interval. If so, find...
Determine whether Rolle's Theorem applies to the following
function on the given interval. If so, find the point(s) that are
guaranteed to exist by Rolle's Theorem. g(x)=x^3- 9 x^2 + 24 x -
20; [2,5]
A)Rolle's Theorem applies and the point(s) guaranteed to exist
is/arex=
(Type an exact answer, using radicals as needed. Use a comma
to separate answers as needed.)
B)Rolle's Theorem does not apply.
2.a Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for...
2.a Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for all
xin an interval ( a , b ), then f is constant on ( a , b
).
b True or False. The product of two increasing functions is
increasing. Clarify your answer.
c Find the point on the graph of f ( x ) = 4 − x 2 that is
closest to the point ( 0 , 1 ).
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then...
Verify that the function satisfies the three hypotheses of
Rolle's Theorem on the given interval. Then find all numbers
c that satisfy the conclusion of Rolle's Theorem. (Enter
your answers as a comma-separated list.)
f(x) = cos(2x), [π/8, 7π/8]
(a) Graph the function
f(x) = x +
7/x
and the secant line that passes through the points (1, 8) and
(14, 14.5) in the viewing rectangle [0, 16] by [0, 16].
(b) Find the number c that satisfies the conclusion of...
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then...
Verify that the function satisfies the three hypotheses of
Rolle's Theorem on the given interval. Then find all numbers
c that satisfy the conclusion of Rolle's Theorem. (Enter
your answers as a comma-separated list.)
f(x) = 1 − 24x +
4x2 ,[2,4]
C=
Rolle's Theorem, "Let f be a continuous function on [a,b] that is differentiable on (a,b) and...
Rolle's Theorem, "Let f be a continuous function on [a,b] that
is differentiable on (a,b) and such that f(a)=f(b). Then there
exists at least one point c on (a,b) such that f'(c)=0."
Rolle's Theorem requires three conditions be satisified.
(a) What are these three conditions?
(b) Find three functions that satisfy exactly two of these three
conditions, but for which the conclusion of Rolle's theorem does
not follow, i.e., there is no point c in (a,b) such that f'(c)=0.
Each...
Does the given function satisfy the three hypotheses of Rolle's Theorem on the given interval? If...
Does the given function satisfy the three hypotheses of Rolle's
Theorem on the given interval? If so, determine where f ′ ( x ) = 0
within the interval; if not, explain which hypotheses are not
satisfied.
Rolle's Theorem Question if f(a)=f(b) then it is constant function, so every point c in the...
Rolle's Theorem Question
if f(a)=f(b) then it is constant function, so every point c in
the interval (a,b) is zero.
I don't understand the terms constant function, is it supposed
to be a horizontal line or it can be a parabola curve.
For example, when f(a)=f(b) and they both exist at the endpoint
then it can be a parabola curve then it break the assumption that
f(a)=f(b) then it is constant function, so every point c in the
interval (a,b)...
Let f be a continuous function on the closed interval [0,1] with a range also contained...
Let f be a continuous function on the closed interval [0,1] with
a range also contained in [0,1]. Prove that f that there exists an
x in [0,1] such that f(x)=x. Is the same explanation still valid if
f is not continuous?
1. Consider how Coase Theorem can be applied to the following scenarios. Specifically, think about the...
1. Consider how Coase Theorem can be applied to the following
scenarios. Specifically, think about the following issues for each
of the scenarios: (i) Are property rights well defined? (ii) Will
trading take place? (iii) Are any of the key assumptions within
Coase Theorem likely to be violated in any way?
a. A chicken farming factory has opened in industrial Unanderra.
The factory produces a foul smell that settles over the center of
Unanderra as well as increased traffic to...
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