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

Chapter problem temperature around the globe.., predict whether there is a ...

predict whether there is a relationship between the mean January temperatures of a city in North America and the city''s position west of the prime meridian.

Prove that 7cot - 3cosec = 3, If 7 cosec?-3cot? = 7, prove that 7cot? - 3co...

If 7 cosec?-3cot? = 7, prove that 7cot? - 3cosec? = 3. Ans:    7 Cosec?-2Cot?=7 P.T 7Cot? - 3 Cosec?=3 7 Cosec?-3Cot?=7 ⇒7Cosec?-7=3Cot? ⇒7(Cosec?-1)=3Cot? ⇒7(C

The sum of the clock, how many times In a 12 hour period will he numbers ad...

how many times In a 12 hour period will he numbers add up to 6? (hint 3:00 is one answer0

Making connections with maths, MAKING CONNECTIONS :  you have read about w...

MAKING CONNECTIONS :  you have read about what the ability to think mathematically involves. In this section we shall discuss ways of developing this ability in children. As yo

Index numbers, What are advantages and disadvantages of both Laspeyres and ...

What are advantages and disadvantages of both Laspeyres and Paasche?

Simple equations, three times the first of the three consecutive odd intege...

three times the first of the three consecutive odd integers is 3 more than twice the third integer. find the third integer.

Triangles, if P is a point in the interior of a triangles ABC,prove that AB...

if P is a point in the interior of a triangles ABC,prove that AB>BC+CA

Statistics, If a mean score is 89 with a standard deviation of 8 points. Wh...

If a mean score is 89 with a standard deviation of 8 points. What is the least score you can make and be in the top 20%?

Fraction, how do you learn about equivelant fractions

how do you learn about equivelant fractions

Find the equation of circle concentric – coordinate geometry, 1. A point P(...

1. A point P(a,b) becomes (3,c) after reflection in x - axis, and (d,6) after reflection in the origin. Show that a = 3, b = - 6, c = 6, d = 2 2. If the pair of lines ax² + 2pxy

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