Show that if f(x) > 0 on (a, b) (that is, if f is convex on [a,

Question:

Show that if fʹʹ(x) > 0 on (a, b) (that is, if f is convex on [a, b]), then for any natural numbers m, n we have Mn(f) < ∫ba f(x)dx < Tm(f): If fʹʹ(x) < 0 on [a, b], this inequality is reversed.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

See More Books

Question Posted: Apr 07, 2016 11:06 AM

See More Questions

Show that if f (2) = 5 and f(x) 10 for x > 2, then f (x) 10x 15 for all x > 2.
Show that if f (x) = ax3 + bx2 + cx + d, then f(k) = r, where r = ak3 + bk2 + ck + d, using long division. In other words, verify the Remainder Theorem for a third-degree polynomial function?
Show that if f (x) and g(x) are functions from the set of real numbers to the set of real numbers, then f (x) is (g(x)) if and only if there are positive constants k, C1, and C2 such that C1 |g(x)|...
5. Explain how Culture can help companies set legal and ethical standards?
Amenity, Inc., was incorporated with 1 million authorized shares, which were issued to Capital General Corporation (CGC) for $2,000. CGC distributed 90,000 of those shares to about 900 of its...
The Dybvig Corporations equity has a beta of 1.3. If the riskfree rate is 4.5 per cent and the expected return on the market is 12 per cent, what is Dybvigs cost of equity capital?
With reference to the discussion on page 492, calculate the CUSUM using 2.25 in place of 2.00 as the centering value. Also make the CUSUM chart. Data From Page 492 5 S -5- 0 5 5 10 15 20 CUSUM chart...
Rice Company performed services on account for $30,000 in 2013, its first year of operations. Rice collected $24,000 cash from accounts receivable during 2013 and the remaining $6,000 in cash during...
Mid-South Auto Leasing leases vehicles to consumers. The attraction to customers is that the company can offer competitive prices due to volume buying. On September 30, 2024, the company leased a...
The date is January 10, 2023, and Maryton Hotels CFO George Smith is looking with dismay at his companys financial performance during 2022. Already facing stiff competition from other hotel chains as...
Note that 10 (1 - x2)1/2 dx = p/4. Explain why the error estimates given by formulas (4), (7), and (10) cannot be used. Show that if h(x) = (1 - x2)1/2 for x in [0, 1], then Tn(h) < /4 < Mn(h)....
Show that lim((cos x)2n) exists for all x R. What is its limit?
(a) Find the functions domain, (b) Find the functions range, (c) Describe the functions level curves, (d) Find the boundary of the functions domain, (e) Determine if the domain is an open region, a...
How does Volatility affect Market Behavior? Do you think that understanding volatility would help you in making decisions when investing? How? And explain the Why?
Distinguish between DNA and RNA with regard to chemical composition, nucleotides included in each, location in the cell and function.
What is exchange control? Discuss its effects on the availability of 'local' capital in Kenya?
1) In the first table, there are missing values for direct and cross rates. Please fill them out (using the available rates, you need to derive the missing rates). 2) In the second table, you need to...
What is the net reaction of the pentose phosphate pathway? Explain
What do you think of Toyotas eight-step problem-solving model? Do you think you could use it at any of the employers where you have held part-time jobs or internships as a student? Why?
Study the pictures/images below. Obviously these was focus on LT sociology, anthropology and poltical science. Try to do some analysis by finding clues that are synonymous with the main concepts....
Find the area of each triangle or rectangle 1. 2. 4.4 feet i -17 feet- 1.2 miles mile
The ten tallest buildings in the world, completed as of the start of 2012, are listed in the following table. Use this table to answer following Exercises. If necessary, round results to one decimal...
For below Exercises, the grades are given for a student for a particular semester. Find the grade point average. If necessary, round the grade point average to the nearest hundredth. 1. 2. Grade...
What is the expected rate of return on a project that requires an investment of $106 today and generates cash inflows of $7, $17 and $122 in each of the next 3 years?
A trader opens a new position by writing two put option contracts. Each contract is on 100 shares of Exxon Mobil common stock. The option premium is $6.06, the strike price is $50, and the stock...
On a particular day, there were 300 stocks that advanced on the NYSE and 800 that declined. The volume in advancing issues was 1000 and the volume in declining issues was 3000. What is the common...

Show that if f(x) > 0 on (a, b) (that is, if f is convex on [a,

Question:

Step by Step Answer:

Use the fact that fx 0 in 4 and 7 Geometrically t...View the full answer

Introduction to Real Analysis

Students also viewed these Calculus questions