Question: A number a is called a fixed point of a function f if f (a) = a. Prove that if f(x) 1 for all real

A number a is called a fixed point of a function f if f (a) = a. Prove that if f’(x) ≠ 1 for all real numbers x, then has f at most one fixed point.

Step by Step Solution

★★★★★

3.42 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Assume that f is differentiable and hence continuous on R and that fx 1 for all z Suppose has m... View full answer

blur-text-image
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)

Word file Icon

M-C-D (335).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

A fixed point of a function f is a number in its domain such that f(c) = c. (The function doesnt move ; it stays fixed.) (a) Sketch the graph of a continuous function with domain [0, 1] whose range...

Q:

A number b is called an upper bound for a set S of numbers if x s b for all x in S. For example 5, 6.5, and 13 are upper bounds for the set S = {1,2,3, 4, 5}. The number 5 is the least upper bound...

Q:

Suppose f is differentiable for all real numbers with f(0) = -3, f(1) = 3, f'(0) = 3, and f'(1) = 5. Let g(x) = sin (f(x)). Evaluate the following expressions. a. g'(0) b. g'(1)

Q:

Question 5 ( 1 0 pts ) . A number a is called a fixed point of a function f if f ( a ) = a . Prove that any continuous function with domain 0 , 1 and range in 0 , 1 must have a fixed point.

Q:

36. A number a is called a fixed point of a function f if f(a) = a. Prove that if f'(x) # 1 for all real numbers x, then f has at most one fixed point.17-18 Show that the equation has exactly one...

Q:

A number a is called a fixed point of a function f if f (a) = a. Prove that if f'(x) 1 for all real numbers x, then f has at most one fixed point.

Q:

Please help me answer these questions! Q1: Preview A number a is called a fixed point of a function f iff(a) - a. Consider the function f (x) = x35 + 5x+ 1, withx ER. (a) Use the Mean Value Theorem...

Q:

Q1: Preview A number a is called a fixed point of a function f if f(a) - a. Consider the function f (x) = x35 + 5x + 1, withx ER. (a) Use the Mean Value Theorem to show that f( x) cannot have more...

Q:

Please help me with the following questions Q1: Preview A number a is called a fixed point of a function f iff(a) - a. Consider the function f(x) = x35 + 5x + 1, withx ER. (a) Use the Mean Value...

Q:

I need help understanding and solving these problems. PLEASE SHOW ALL WORK so I can learn from it. Thank you 10 Problems in all Section 1.0#8 8. The gure below shows the composite develop- mental...

Q:

Atlantic Service Company was established in Moncton, New Brunswick, five years ago to provide services to the home construction industry. It has been very successful, with assets, sales, and profits...

Q:

After the oil spill in the Gulf of Mexico, Bob Dudley was appointed as British Petroleums first American CEO. In a speech to business leaders in London, Dudley said the following in his closing...

Q:

Cash and cash equivalents, as used on the statement of cash flows, consist of: Question 4 options: currency, bank accounts, and all investments currency, bank accounts and short - term, highly liquid...

Q:

The A-1 Corporation supplies airplane manufacturers with preformed sheet metal panels that are used on the exterior of aircraft. Manufacturing these panels requires only five sheet metal??forming...

Q:

Pricing in imperfect markets (continuation of 22-28). Refer to Problem 22-28. 1.Suppose the manager of Division A has the option of (a) cutting the external price to $195, with the certainty that...

Q:

The weight of a rectangular block of low-density material is 15.0 N. With a thin string, the center of the horizontal bottom face of the block is tied to the bottom of a beaker partly filled with...

Q:

Changing end temperatures assume that the ends of the bar in Probs. 5 9 have been kept at 100oC for a long time. Then at some instant, call it t = 0, the temperature at x = L is suddenly changed to...

Q:

Suppose that in Exercise 9-25 we wanted to reject the null hypothesis with probability at least 0.8 if mean strength = 3500. What sample size should be used?

Q:

1. List four reasons why indirect costs are allocated.

Q:

What does the affidavit released from the PMO say about Netaji?

Q:

using above information answer following question: 1.What price could Jennifer afford to pay if she only needs is a 9% (unleveraged) yield? 2.Under what type of circumstances might Jennifer pay that...

Q:

Terri Simmons is single and had $174,500 in taxable income. Use the rates from Table 2.3. a. Calculate her income taxes. (Do not round intermediate calculations and round your answer to the nearest...