Estimate Error: How Did He Get 4?

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Homework Help Overview

The discussion revolves around understanding the behavior of the function f(x) = sin(2x) and its derivatives, particularly focusing on the second derivative and its maximum value. Participants are attempting to clarify how a specific value, 4, was derived in relation to the problem.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are exploring the properties of the sine function, particularly its range and behavior when differentiated. Questions are raised about the maximum values of the second derivative and the implications of the function's oscillation.

Discussion Status

Some participants have provided insights regarding the oscillation of the sine function and its derivatives, while others are seeking clarification on the specific value of 4 and its derivation. There appears to be a productive exchange of ideas, though no consensus has been reached.

Contextual Notes

There is a reference to a specific image that may contain additional context or information relevant to the problem, but it is not accessible in the discussion. Participants are also considering the implications of the function's behavior within a defined interval.

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The function is f(x) = sin(2x). Find f'(x) and then f''(x). What is the largest possible value of f''(x)?
 
so because sin 2x cannot be more than 1 between the pi/2 and 0??
 
sin(x) oscillates between -1 and 1. Check on the TI.

Also, sin(nx) , such as sin(3x) , just increases the frequency I think. You can graph that too. It just squooshed the oscillations closer to the y-axis. So they are still in between -1 and 1.
 
o ok i got it thanks
 

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