Let I (a, b) and f I R We say that f is ' 'locally increasing ' ' at c I if there exists 0 such that f is increasing on I (c (c), c (c)) Prove that if f is locally increasing at every point of I, then f is increasing on I

Question: Let I := (a, b) and f : I R. We say that f is ''locally increasing'' at c I if there exists

Let I := (a, b) and f : I → R. We say that f is ''locally increasing'' at c ∈ I if there exists δ© > 0 such that f is increasing on I ∩ (c - δ(c), c + δ(c)). Prove that if f is locally increasing at every point of I, then f is increasing on I.

Step by Step Solution

★★★★★

3.44 Rating (154 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The hypothesis that f is locally increasing presents us with a gauge If x i 1 x i ... 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)

829-C-F-M (399).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Let d be a gauge on I: = (a, b) and suppose that I does not have a d-fine partition. (a) Let c : = (a + b). Show that at least one of the intervals [a, c] and [c, b] does not have a -fine partition....

For f, g: Z+ R, we say that f is "big Theta of g," and write f (g), when there exist constants m1, m2 R+ and k Z+ such that m1|g(n)| Prove that f ...

Let I := [a, b] and let f : I R be a (not necessarily continuous) function with the property that for every x I, the function f is bounded on a neighborhood Vx (x) of x (in the sense of Definition...

Give an example of a function f which satisfies the intermediate-value property on a closed and bounded interval [a, b] but is not continuous on a, 6). () Give an example of a function f which is...

Roberge, M. (2015). The right way to use compensation. Harvard Business Review, 93, 70-75. Zehnder, E. (2001). A simpler way to pay. Harvard Business Review, 79, 53-61. 1. Explain how EZI compensates...

Could someone please check my work and let me know if my circled wording is OK Please state all definitions and theorems that you will need: Definition 5.4.1 Let f : D - R . We say that f is...

I know there's a simpler way to solve this problem but could someone please check my work and let me know if it is correct Please state all definitions and theorems that you will need: AI WH...

I know this work is correct but could someone please answer the three questions I have in black ink Please state all definitions and theorems that you will need: Definition 5.4.1 Let f: D - R . We...

Could someone please help me with part two of this problem and check my work for part three. I think part one is ok Theorem 5.4.6 Suppose f: D -+ IR is continuous on a compact sot D Then of is...

Time value Personal Finance Problem You can deposit $13,000 into an account paying 7% annual interest either today or exactly 5 years from today. How much better off will you be at the end of 25...

Suppose that you are vice president of branch services at the Bank of East Lansing. You notice that several branches have consistently low customer service ratings even though there are no apparent...

lem \ # 3 : There is a bond on a company's books with an original term of 1 0 years that was purchased for a premium at its issuance, just over 2 years ago. The bond pays semi - annual interest. With...

Sally loves to receive her coupons from American Eagle. She typically looks in her email every day to see what promotions the company will be sending. The American Eagle sales promotions are helping...

The table shows the top ten popular breeds of dogs in 2012 according to the American Kennel Club. The breeds are listed in the order of number of registrations. 1. Which breed has more dogs...

Check to see whether each number written in standard form matches the number written in words. If not, correct the number in words. See the Concept Check in this section. 1. 2. If a number is written...

For below Exercises, identify which number is the minuend and which number is the subtrahend. See the second Concept Check in this section. 1. 2863 - 1904 2. Find 86 decreased by 25. 3. In your own...

Consider the following cash flows of two mutually exclusive projects for Tokyo Rubber Company. Assume the discount rate for both projects is 10 percent. a. What is the payback period for both...

q26 2 points Save Answer You have purchased a put option on ABC common stock for $3 per contract. The option has an exercise price of $58. What is your net profit on this option if stock price is $46...

Abe Forrester and three of his friends from college have interested a group of venture capitalists in backing their business idea. The proposed operation would consist of a series of retail outlets...