Question: Assume that f and g continuous functionals on [a, b] that are differentiable on the open interval (a, b). Then there exists some x (a,

Assume that f and g continuous functionals on [a, b] Š† „œ that are differentiable on the open interval (a, b). Then there exists some x ˆˆ (a, b) such that

Provided g(a) ‰ g(b) and g€²(x) ‰ 0, this can be written as

f' (x) f (b)-f(a) gx) g(b) -g(a) =

Step by Step Solution

★★★★★

3.46 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Define by and is differentiable on with By Rolle... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

914-M-N-A-O (720).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Suppose that f C[a, b] is differentiable on the open interval (a, b). Then there exists some x (a, b) such that f(b) - f(a) = f[x](b - a)

If f, g are continuous functionals on a metric space X, then f + g is continuous f is continuous for every R Therefore the set of all continuous functionals on X is a linear space.

(a) Verify that y = -1 / (x + c) is a one-parameter family of solutions of the differential equation y' = y 2 . (b) Since f (x, y) = y 2 and Ïf/Ïy = 2y are continuous everywhere, the region...

KINDLY PLEASE DIGITALIZED IT 11- Find the Area between the curve y=x(x-3) and the ordinates x=0 and x=5. Note: (hint) The Graph shows 2 regions. Get first the area of each region before adding it...

Kindly please digitalized the answer 1- Integrate the following. 1. fx'dx 2. JT 3. S(x2 - 2x + 5) dx 4. S(x + 2)5 dx 5. S1+ y2 2ydy 6. S cos(70 + 5) do 7. S ( x2 + 2x - 3)(x + 1) dx 11- Find the Area...

2, Let f (at) and 9(a) be dened for al] a: # a over an interval containing (1. Assume that liming f(a:) = L and limp.\" g(a:) = M. Then the summation law for limits states that mum) + g(x)1= gig me)...

Consider the function given by f ( x ) = { s i n ( x ) i f x > x - i f x ( a ) Identify the real numbers at which f ( x ) is discontinuous. Hint: You should justify why f ( x ) is discontinuous at...

x2 10x + 9 . _ _ ls x) = T differentiable at x = E3? Justrfy your answer. Choose the correct answer below. O A. No. the function is not oi'erentiable because x] is not continuous at x = E3. (:1 B....

Consider a function f that is differentiable at a point a: = a. The tangent line to the graph of f at a is given by the equation 9 = u) + f'(a)($ - [1) Draw a diagram illustrating equation for the...

How does a single-payment or balloon loan differ from an installment loan? What is a bridge loan?

Sustainability involves more than just the impact of actions on the environment. The triple bottom line recognizes that a company has to measure its impact on people, planet, and profit for its long-...

The following is typically considered a long - term financial plan: Group of answer choices Creating a budget this year Investing in a mutual fund for six years to accumulate retirement funds Using...

The R data frame pistonrings,4 available in the R package qcc, consists of 40 samples, each of size 5, of the inside diameter of piston rings for an automotive engine. The first column of the data...

The formula C = 5/9 (F 32), where F > 459.67, expresses the Celsius temperature C as a function of the Fahrenheit temperature F. Find a formula for the inverse function and interpret it. What is...

In the theory of relativity, the mass of a particle with speed is Where mo is the rest mass of the particle and is the speed of light in a vacuum. Find the inverse function of f and explain its...

Find a formula for the inverse of the function. 4-1 24. f(x) = 2 + 3 26. y = 2x + 3 23. f(x) - 10 - 3r 25. f(x) = e 27. y- In(x + 3) 28. v = 1-

5. Mesmer Analytic, a biotechnology firm, floated an initial public offering of 2,000,000 shares at a price of $5.00 per share. The firm's owner/managers held 60 percent of the company's $1.00 par...

Your company is considering the replacement of an old delivery van with a new one that is more efficient. The old van cost $40,000 when it was purchased 5 years ago. The old van is being depreciated...

41. Per the Fraud Examiners Manual, which of the following best describes electronic discovery (aka e-discovery)? A. it refers to an illegal discovery process that is the resulting of hacking into...