Find a,b Parameters for Function to Get Extreme Value

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Homework Help Overview

The discussion revolves around finding parameters \(a\) and \(b\) for the function \(f(x) = \frac{\sin(2x)}{a - b\cos(x)}\) such that it has an extreme value at the point \((\frac{\pi}{3}, \frac{1}{4})\). The problem involves calculus concepts related to derivatives and extreme values.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the necessity of setting the derivative to zero at the specified point and whether to also set the function equal to \(\frac{1}{4}\) to find the parameters. There is mention of needing to derive a relationship between \(a\) and \(b\) using the given function value.

Discussion Status

Some participants have provided guidance on the approach to take, suggesting the need to use both the derivative condition and the function value to determine the parameters. There is an indication that multiple interpretations of the problem are being explored, particularly regarding the relationship between \(a\) and \(b\).

Contextual Notes

Participants are navigating the constraints of the problem, including the need to satisfy both the derivative condition and the function value at the specified point. There is an emphasis on the importance of correctly interpreting the conditions for extreme values.

Fatlum
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Find a, b parameters such that the function such that the function $f(x)= (sin2x)/(a-bcosx)$ has extreme value in point (pi/3,1/4)
 
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Welcome to PF!

Hi Fatlum! Welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
I understand that in this point the derivative should be 0. So I found the derivative ,equaled to zero and I replaced (pi/3=x) . But I'm not sure, should I equal the function with 1/4 to find the ordiante ?
 
using only sinx = π/3 will only give you the ratio a/b

you need to use y = 1/4 to find what they actually are :smile:
 
Thank you very much tiny-tim. I found now the paramters. a=5 and b=4.
 

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