Critical Points of a trig function

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Homework Help Overview

The discussion revolves around finding the critical points of a trigonometric function involving sine, specifically the function -sin(x) + (1/2)sin(2x). Participants are examining the correctness of identified critical points and the differentiation process involved.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning the differentiation of the function and the validity of the critical points identified. There is a discussion about applying the zero product property to find solutions, as well as clarifying the form of the derivative.

Discussion Status

The discussion is ongoing with some participants confirming and questioning the correctness of the critical points. There is a mix of agreement and disagreement regarding the identified points, and clarification on the derivative has been provided.

Contextual Notes

There appears to be some confusion regarding the correct form of the derivative and the critical points, with participants revisiting their assumptions and calculations.

realism877
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Trig function:-sinx+(1/2)sin2x(2)

The criticial points are (pi), (pi/3), and (5pi/3).

Am I correct?
 
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Is that the first derivative there, or is it not differentiated?
[tex]-sin(x)+2sin(2x)[/tex]
 
Yes, the first derivative.
 
Well,
Given that [itex]sin(2x) = 2sin(x)cos(x)[/itex], you could say the following:
[itex]4sin(x)cos(x)-sin(x)=0[/itex]
[itex]sin(x)(4cos(x)-1)=0[/itex]
Using the zero product property, what are the solutions to that?
 
I just want to know if my critical points are correct or not.
 
No, they are not
 
Is pi/2 a point instead of pi?
 
I'm sorry.

The derivative is sin2x-sinx
 
realism877 said:
I'm sorry.

The derivative is sin2x-sinx

In that case you were right.
 

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