1. Given the function f(x) x-4x(a) Determine if the function x) defined onTheorem. If so, find the value "c" guaranteed by Rolle's Theorem and interpret itsmeaning. If not, explain why not.[0, 4] satisfies the conditions of Rolle's(b) Determine if the function fx) defined onTheorem. If so, find the value "c" guaranteed by Rolle's Theorem and interpret itsmeaning. If not, explain why not.[0, 2] satisfies the conditions of Rolle's

Question
Asked Aug 11, 2019
8 views
1. Given the function f(x) x-4x
(a) Determine if the function x) defined on
Theorem. If so, find the value "c" guaranteed by Rolle's Theorem and interpret its
meaning. If not, explain why not.
[0, 4] satisfies the conditions of Rolle's
(b) Determine if the function fx) defined on
Theorem. If so, find the value "c" guaranteed by Rolle's Theorem and interpret its
meaning. If not, explain why not.
[0, 2] satisfies the conditions of Rolle's
help_outline

Image Transcriptionclose

1. Given the function f(x) x-4x (a) Determine if the function x) defined on Theorem. If so, find the value "c" guaranteed by Rolle's Theorem and interpret its meaning. If not, explain why not. [0, 4] satisfies the conditions of Rolle's (b) Determine if the function fx) defined on Theorem. If so, find the value "c" guaranteed by Rolle's Theorem and interpret its meaning. If not, explain why not. [0, 2] satisfies the conditions of Rolle's

fullscreen
check_circle

Expert Answer

Step 1

a) To check whether the given function satifies the Rolle\\\\\\'s theorem over the interval [0, 4] or not.

f (x)x-4x:[0,4]
[0,4
f(x) is continuous on
(x) is differentiable on (0,4)
f(0) 0
f(4)(4)4(4)64-16 48
(0) (4)
Then the Rolle's theorem does not satifies for the function
f (x)x-4x over the interval [0,4]
Since the conditions of theorem fails to satisfies, the value of c cannot be obtained.
help_outline

Image Transcriptionclose

f (x)x-4x:[0,4] [0,4 f(x) is continuous on (x) is differentiable on (0,4) f(0) 0 f(4)(4)4(4)64-16 48 (0) (4) Then the Rolle's theorem does not satifies for the function f (x)x-4x over the interval [0,4] Since the conditions of theorem fails to satisfies, the value of c cannot be obtained.

fullscreen
Step 2

b) To check whether the given function satifies the Rol...

f (x)4x 0,2
-/(x) is Continuous on [0,2
f(x) is differentiable on (0,2)
f()0
f(2) (2)4(2) 8-8 0
(0) f(2)
Then the Rolle's theorem satifies for the function
f(x) x3-4x over the interval [0,2]
help_outline

Image Transcriptionclose

f (x)4x 0,2 -/(x) is Continuous on [0,2 f(x) is differentiable on (0,2) f()0 f(2) (2)4(2) 8-8 0 (0) f(2) Then the Rolle's theorem satifies for the function f(x) x3-4x over the interval [0,2]

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Derivative

Related Calculus Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Calculate the directional derivative in the direction of v at the given point. fx, v)- tan Cy). -(1,...

A:  The partial derivatives of f(x,y) at the point (x,y)=(5,2)are:

question_answer

Q: If y (x25x-1)e2x then y (3x2-10x+7)e2x O (2.7x+4)e2x O(22+ 12x + 3)e2x (2x+5)32x (2x 52-1

A: Given, 

question_answer

Q: The total profit (in dollars) from the production and sale of x calendars if P(x)= 22x-0.02x2-500; 0...

A: It is given that, the total profit from the production and sale of x calendar is P(x)=22x–0.02x2–500...

question_answer

Q: Find y' if x^y = y^x .

A: Given, 

question_answer

Q: The graphs of y=1.1x and y=x have two points of intersection, while the graphs of y=2^x and y=x have...

A: Here, we are given that for a real number 1< p < 2 , the graphs of y=px and y=x have exactly o...

question_answer

Q: 7n 5-4n For the following answer blanks, decide whether the given sequence or series is convergent o...

A: (a)we are given a series as 

question_answer

Q: If the marginal revenue(in dollars per unit) for a month is given by MR'= -0.006x+36, find the total...

A: The marginal revenue for a month is MR′ = -0.006x + 36.The total revenue from the production and sal...

question_answer

Q: Evaluate the integral.   Integral from nothing to nothing hyperbolic cotangent StartFraction x Over ...

A: Refer to the integral,Rewrite the hyperbolic cotangent as,

question_answer

Q: Determine the following indefinite integral. 324 dx, x> In 18 A dx 324- e2x Type an exact answer. Us...

A: The given integral is,