Question

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 on the given interval?

f(x) = 4x^{2} − 5x + 3, [0,
2]

3a) If it satisfies the hypotheses, find all numbers *c*
that satisfy the conclusion of the Mean Value Theorem. (Enter your
answers as a comma-separated list. If it does not satisify the
hypotheses, enter DNE).

c =

4) Find the number *c* that satisfies the conclusion of
the Mean Value Theorem on the given interval. (Enter your answers
as a comma-separated list. If an answer does not exist, enter
DNE.)

f(x) = square root x

c=?, [0,25]

4b) Graph the function, the secant line through the endpoints, and the tangent line at (c, f(c)).

4c) Are the secant line and the tangent line parallel?

Yes or No?

Answer #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 − 24x +
4x2, [2, 4]

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) = 5 − 18x + 3x^2, [2, 4]
c=

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) = 7 − 24x + 2x^2, [5, 7]

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) = 7 − 8x +
2x2, [1, 3]

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.)
a) f(x)= x^3-x^2-12x+5 , [0,4]
b) f(x)= square root/x - 1/7x , [0,49]
c) fx)= cos(3x), [pi/12,7pi/12]

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,...

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...

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...

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...

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]

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago