Question
In: Math
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.
Solutions
milcah answered 2 years agoRelated Solutions
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.
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=
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...
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)...
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)...
Check the hypotheses of Rolle's Theorem and the mean value theorem and find a value of...
Check the hypotheses of Rolle's Theorem and the mean value
theorem and find a value of c that makes the appropriate conclusion
true. Illustrate the conclusion with a graph:
Prove that x^4+6x^2-1=0 has exactly two solutions
Please provide all work needed to solve the problem with
explanations. Thank you!
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...
Find (without using a calculator) the absolute extreme values of the function on the given interval....
Find (without using a calculator) the absolute extreme
values of the function on the given interval.
f(x) = 3x2 − x3 on [0, 3]
find the average rate of change of the function over the given interval. answer must be...
find the average rate of change of the function over the given
interval. answer must be in radian ... pls explain the steps ty
h(t)= cot t
a) [5pi/4, 7pi/4]
b) [5pi/6, 3pi/2]
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