What is the maximum value of b for a given function with certain properties?

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In summary, the conversation discusses a problem involving finding the greatest value of b for a given function f that satisfies certain properties. The suggested solution involves using the Taylor series with the remainder in the form using the Mean Value Theorem. The correct answer is determined to be D (12).
  • #1
lhuyvn
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Hi All,

I have a problem, and it is so confusing to me. I put it here in the hope of getting some helps to make it clear.

Thank you,

the problem is given below.

What is the greatest value of b for which any real valued function f that satisfies the following properties mus also satisfy f(1)<5

i) f is infinitively differentiable on the real numbers.
ii)f(0)=1, f'(0)=1, f"(0)=2
iii)|f'''(x)|<b for all x in [0,1]

A.1
B.2
C.6
D.12
E.24
 
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  • #2
I would suggest looking at the Taylor series with the remainder in the form using the Mean Value Theorem, which ever one that is.
 
  • #3
Oh, It is so wonderful suggestion !

So, it is solved. The correct answer is D (12)
 

Related to What is the maximum value of b for a given function with certain properties?

1. What is a functional question?

A functional question is a type of inquiry that focuses on understanding how a system or process works and how it can be improved or optimized. It seeks to identify the purpose, components, and functions of a system in order to gain a deeper understanding of its functionality.

2. How is a functional question different from a research question?

A functional question is more specific and focused on understanding the inner workings of a system, while a research question is broader and seeks to investigate a topic or phenomenon. A functional question is often used in scientific research to inform the development of hypotheses and experiments.

3. Can a functional question be answered through observation or experimentation?

Yes, a functional question can be answered through observation or experimentation. In fact, these methods are often necessary to gain a thorough understanding of the functions and components of a system.

4. What are some examples of functional questions?

Examples of functional questions include: How does the human digestive system break down food? What is the role of enzymes in cellular metabolism? How does the circulatory system deliver oxygen to different parts of the body?

5. Why are functional questions important in scientific research?

Functional questions are important in scientific research because they help scientists gain a deeper understanding of how systems and processes work. This knowledge can then be used to inform further research, improve existing systems, and develop new technologies.

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