Question: For the function f(x) = 2x at the interval [1,4], the Mean Value Theorem says that: a. At least a real number c exists at

For the function f(x) = 2x at the interval [1,4], the Mean Value Theorem says that: a. At least a real number c exists at the interval [1,4] where: f'(x) = ( f(4) - f(1) ) / ( 4 - 1 ) b. At least a real number c exists at the interval (1,4) where: f'(x) = ( f(4) - f(1) ) / ( 4 - 1 ) c. At least a real number c exists at the interval [1,4] where: f'(x) = 0. d. At least a real number c exists at the interval (1,4) where: f'(x) = 0

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Econ 289 Assignment 2 (Sections 4.1-4.5) Questions Solve all questions, showing your work in reasonable detail. Finish your calculations: when the results can be reduced to numbers, calculate those...

Consider the function below. f (x) = x (x2 - 4x - 9) Determine whether the Mean Value Theorem can be applied to f on the closed interval [-1, 1]. (Do this on paper. Your instructor may ask you to...

Suppose f (x) = x 3 + 2x 2 x + 6. From calculus, the Mean Value Theorem guarantees that there is at least one number in the open interval ( 1, 2) at which the value of the derivative of f, given by...

1. Find the domain of the function f ( x )= x 2 x +2 1) ______ (A) D=( ,2 ) ( 2, ) (B) D=( ,2 ) (2, ) (C) D= ( 2, ) (D) D=(2, ) (E) none of the above 1 2. According to the Center for Disease Control...

\f2 of 10 Find the values of x that are critical numbers of the function f (x) = 3x* - 1623 + 6x2 + 72x + 1. Item (1 point) Item 2 O z= -31 = -2, and z =-1 Item 3 O z = -3,1= -2, and x = 1 Item 4 O r...

I was wondering if someone could help me answer the four questions below. Please solve the problems fully with work shown. Thank you in advance. 12. Given that f (x) = (2x - 3) and f (1) = -1, if g...

Practice Exam 1 1. (19 total points) PROBABILITY CALCULATIONS Let X be a continuous random variable with probability density function f (x) = 3x2 , for 0 x 1 . 2.0 1.0 0.0 f(x) = 3x2 3.0 Here is a...

This Test: 17 pts possible Show that the function r(8) = 0 + sin 3 - 8 has exactly one zero in the interval ( - 00,00). Rolle's Theorem states that for a function f(x) that is continuous at every...

Lastname: Firstname: Be certain to show all work manually on these sheets, scan and return for full credit. Math-2412.WS1 Due: Wed, Jun 14 Prof: Bock LAB #1 1a. A sheet of cardboard 3 ft by 8 ft is...

PREPARE JOURNAL ENTERIES TO RECORD EACH OF THE FOLLOWING EVENTS. 1.TOM'S TAX PREP'S MONTHLY RENT IS $3500, AT THE OF FEBRUARY, THEY HAD NOT YET RECEIVED THEIR MONTHLY RENT INVOICE. 2.IN EARLY MARCH ,...

Certain E. coli bacteriophages encode a protein called Q, which binds to RNAP shortly after transcription initiation, before 70 is released. Q increases the rate of transcription and renders RNAP...

List products that do NOT have a NULL value in the NULLFieldExample column

Please answer both!!! WT has been purchasing printers from a particular company for years and it is need to purchase some new printers for the library, While working on this purchase, udministration...

The permanence rule: We tend to have more confidence in information that is of a more permanent nature than information that is of a temporary nature.

The official stamp rule: We tend to have more confidence in information that is exempt from the Freedom of Information Act than if the same information was made readily available.

4. Based on a message you have recently received, analyse it in relation to its three components: a. the information component, b. its relational component and c. its hierarchical component.