The mean value theorem, Mathematics

Assignment Help:

The Mean Value Theorem : In this section we will discuss the Mean Value Theorem. 

Before we going through the Mean Value Theorem we have to cover the following theorem.

Rolle's Theorem : Assume f ( x ) is a function which satisfies all of the following.

1. f ( x ) is continuous on the closed interval [a,b].

2. f ( x ) is differentiable on the open interval (a,b).

3. f ( a ) =f (b )

Then there is a number c such that a < c < b and f ′ (c ) = 0 .  Or, in other terms f ( x ) contain a critical point in (a,b).

 


Related Discussions:- The mean value theorem

Fundamental theorem of calculus, Fundamental Theorem of Calculus, Part I ...

Fundamental Theorem of Calculus, Part I As noted through the title above it is only the first part to the Fundamental Theorem of Calculus. The first part of this theorem us

Fundamental theorem of integral facts , Fundamental Theorem of Calculus, Pa...

Fundamental Theorem of Calculus, Part II  Assume f(x) is a continuous function on [a,b] and also assume that F(x) is any anti- derivative for f(x). Hence, a ∫ b f(x) dx =

Practical geometry, Ask question draw a line parallel to given line xy at a...

Ask question draw a line parallel to given line xy at a distance of 5cm from it #Minimum 100 words accepted#

Definition of vertical asymptote, Vertical asymptote Definition : The funct...

Vertical asymptote Definition : The function f(x) will contain a vertical asymptote at x = a if we contain any of the following limits at x = a .   x→a- Note as well that it

Determine the length of the diagonal, A box is 30 cm long, 8 cm wide and 12...

A box is 30 cm long, 8 cm wide and 12 cm high. Determine the length of the diagonal AB ? Round to the nearest tenth. a. 34.5 cm b. 32.1 cm c. 35.2 cm d. 33.3 cm

How many 6-inch tiles are required to tile the floor, Mark intends to tile ...

Mark intends to tile a kitchen floor, which is 9 by 11 ft. How many 6-inch tiles are required to tile the floor? a. 60 b. 99 c. 396 c. Since the tiles are calculated in

Tangent, Tangent, Normal and Binormal Vectors In this part we want to ...

Tangent, Normal and Binormal Vectors In this part we want to look at an application of derivatives for vector functions.  In fact, there are a couple of applications, but they

Detremine the rectilinear distance, Rectilinear Distance (Total Travel Dist...

Rectilinear Distance (Total Travel Distance per Day Using Rectilinear Distance): It can be computed through using following formula: d(X, Pi) = |x - ai| + |y - bi| (Source: T

Mean, a data set has a mean of 3, a median of4, and a mode of 5, which numb...

a data set has a mean of 3, a median of4, and a mode of 5, which number must be in the data set 3,4,or5

Determine the area of the walkway, Mark is preparing a walkway around his i...

Mark is preparing a walkway around his inground pool. The pool is 20 by 40 ft and the walkway is intended to be 4 ft wide. Determine the area of the walkway? a. 224 ft 2 b.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd