How to find local max and min points for y = sinxcox^3x

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Homework Help Overview

The problem involves finding the local maximum and minimum points for the function y = sin(x)cos^3(x). Participants are discussing the necessary steps to analyze the function's derivatives.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to find the first and second derivatives of the function. There is uncertainty about the correctness of the derivatives and the subsequent steps to take after finding them. Questions arise regarding the application of the product rule and how to solve the resulting equations.

Discussion Status

Some participants have confirmed the derivative obtained by the original poster, while others are discussing how to set the derivative equal to zero and solve for x. There is an ongoing exploration of different equations derived from the first derivative, with some participants expressing difficulty in progressing from certain equations.

Contextual Notes

There is a mention of confusion regarding the manipulation of the equation cos^2(x) - 3(1 - cos^2(x)), indicating potential assumptions or missing information that could affect the problem-solving process.

cruisx
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Homework Statement



Hey, so i need some help trying to find the local max and min points for y = sinxcox3x

Homework Equations



The Attempt at a Solution


I know i need to find the first and 2nd derivative but i do not know if i am doing it right. I also do not know what to do after wards.

my first derivative ends up being cos^2x(cos^2x - 3sin^2x)
what do i do after this to solve my question. Help would be appreciated.
 
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You need to find the first derivative and check the values of x when Dy = 0 - so set your derivative to 0 and solve for x.
I did not check your derivative. Did you apply the product rule?
 
I got the same derivative.
 
Yes my derivative is cos^2x(cos^2x - 3sin^2x) so do i do

0 = cos^2x or 0 =cos^2x - 3sin^2x)

and solve for both?
 
Yup you solve both
 
VeeEight said:
Yup you solve both

Ok so i got the values for the left but the right eqn is nto going well. I do not understand what to do after cos^2x - 3(1-cos^2x)
 
cruisx said:
Ok so i got the values for the left but the right eqn is nto going well. I do not understand what to do after cos^2x - 3(1-cos^2x)
cos^2 x- 3 sin^2 x= cos^2 x- 3(1- cos^2 x)= cos^2 x- 3+ 3cos^2 x= 0
so 4cos^2 x= 3, cos^2(x)= 3/4.
 

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