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

Using euclid''s algorithm find the value of x & y, If d is the HCF of 30, 7...

If d is the HCF of 30, 72, find the value of x & y satisfying d = 30x + 72y. (Ans:5, -2 (Not unique) Ans:    Using Euclid's algorithm, the HCF (30, 72) 72 = 30 × 2 + 12

Standardizing a random variable, Standardizing a Random Variable       ...

Standardizing a Random Variable       If X is a random variable with E(X) = m and V(X) = s 2 , then Y = (X – m)/ s is a random variable with mean 0 and standard deviatio

Explain how to distribute simplifying expressions, Explain How to Distribut...

Explain How to Distribute simplifying expressions? The distributive law states that for all numbers a, b, and c, a(b + c)= ab + ac What does this mean in plain language?

Solve 8 cos2 (1 - x ) + 13 cos(1 - x )- 5 = 0 trig function, Solve 8 cos 2 ...

Solve 8 cos 2 (1 - x ) + 13 cos(1 - x )- 5 = 0 . Solution Now, as specified prior to starting the instance this quadratic does not factor.  Though, that doesn't mean all i

Prove that rb is a tangent to the circle, QR is the tangent to the circle w...

QR is the tangent to the circle whose centre is P. If QA ||  RP and AB is the diameter, prove that RB is a tangent to the circle.

Even and odd functions, Even and Odd Functions : This is the final topic ...

Even and Odd Functions : This is the final topic that we have to discuss in this chapter.  Firstly, an even function is any function which satisfies,

Construct a tangent to a circle of radius, 1.  Draw a pair of tangents to a...

1.  Draw a pair of tangents to a circle of radius 2cm that are inclined to each other at an angle of 900. 2.  Construct a tangent to a circle of radius 2cm from a point on the c

Solve the extraneous solutions, Solve the Extraneous Solutions ? You're...

Solve the Extraneous Solutions ? You're worst enemy (aside from arithmetic mistakes), while you're trying to solve a rational equation, is forgetting to check for extraneous so

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