Question
In: Math
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 the
Mean Value Theorem for this function f and the interval
[1, 14].
c =
Solutions
milcah answered 2 years agoRelated Solutions
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=
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.
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.
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!
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...
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...
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)...
Show step by step to understand 1.Verify that the hypotheses of the Mean-Value Theorem are satisfied...
Show step by step to understand
1.Verify that the hypotheses of the Mean-Value Theorem are
satisfied for the function ?(?) = (√(? − 1) + 1) on the interval
[2,10], and find all values of ? in the given interval that satisfy
the conclusion of the theorem.
2. Verify that the hypotheses of the Rolle’s Theorem are
satisfied for the function ?(?) = (?^2−1)/(?−2) on the interval
[−1,1], and find the value of ? in the given interval that satisfy...
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)...
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 ).
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