Question

A function f(x) and interval [a,b] are given. Check if the Mean Value Theorem can be applied to f on [a,b]. If so, find all values c in [a,b] guaranteed by the Mean Value Theorem Note, if the Mean Value Theorem does not apply, enter DNE for the c value. f(x)=−3x2+6x+6 [4,6]

Answer #1

A function f(x) and interval [a,b] are given. Check if the Mean
Value Theorem can be applied to f on [a,b]. If so, find all values
c in [a,b] guaranteed by the Mean Value Theorem
Note, if the Mean Value Theorem does not apply, enter
DNE for the c value.
?(?)=11?^2−5?+5 on [−20,−19]
What does C=?

Does the function satisfy the hypotheses of the Mean Value
Theorem on the given interval? f(x) = 3x2 + 3x + 6, [−1, 1]
No, f is continuous on [−1, 1] but not differentiable
on (−1, 1).
There is not enough information to verify if this function
satisfies the Mean Value Theorem.
Yes, it does not matter if f is continuous or
differentiable; every function satisfies the Mean Value
Theorem.
No, f is not continuous on [−1, 1].Yes, f is...

Does the function satisfy the hypotheses of the Mean Value
Theorem on the given interval?
f(x) = x3 + x − 9, [0, 2]
Yes, f is continuous on [0, 2] and differentiable on
(0, 2) since polynomials are continuous and differentiable on .No,
f is not continuous on [0, 2]. No,
f is continuous on [0, 2] but not differentiable on (0,
2).Yes, it does not matter if f is continuous or
differentiable; every function satisfies the Mean Value
Theorem.There is...

1aDoes the function satisfy the hypotheses of the Mean Value
Theorem on the given interval?
f(x) = 4x2 + 3x + 1, [−1,
1]
a.No, f is continuous on [−1, 1] but not differentiable
on (−1, 1).
b.Yes, it does not matter if f is continuous or
differentiable; every function satisfies the Mean Value
Theorem.
c.Yes, f is continuous on [−1, 1] and differentiable on
(−1, 1) since polynomials are continuous and differentiable on
.
d.No, f is not continuous on...

Determine whether the Mean Value theorem can be applied to
f on the closed interval
[a, b].
(Select all that apply.)
f(x) =
8 − x
, [−17, 8]
Yes, the Mean Value 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).
None of the above.
If the Mean Value Theorem can be applied, find all values of
c in the open...

Determine whether the Mean Value theorem can be applied to f
on the closed interval [a, b]. (Select all that apply.) f (x) = x7,
[0,1] Yes, the Mean Value Theorem can be applied. No, f is not
continuous on [a, b]. No, f is not differentiable on (a, b). None
of the above. If the Mean Value Theorem can be applied, find all
values of c in the open interval (a, b) such that f ‘(c) = f (b)...

1. Does the function satisfy the hypotheses of the Mean Value
Theorem on the given interval?
f(x) = x3 + x − 5, [0, 2]
a) No, f is continuous on [0, 2] but not differentiable
on (0, 2).
b) Yes, it does not matter if f is continuous or
differentiable; every function satisfies the Mean Value
Theorem.
c) There is not enough information to verify if this function
satisfies the Mean Value Theorem.
d) Yes, f is continuous on [0,...

1) 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 − 12x + 2x^2, [2, 4]
c =
2) If f(2) = 7 and f '(x) ≥ 1 for 2 ≤
x ≤ 4, how small can f(4) possibly be?
3) Does the function satisfy the hypotheses of the Mean Value
Theorem...

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...

Verify that the function satisfies the hypotheses of the Mean
Value Theorem on the given interval. Then find all numbers c that
satisfy the conclusion of the Mean Value Theorem.
f(x) = e^-x , [0,2]

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