What is the derivative of f(x) = 2cos3x + 3sin2x on the interval (-pie, pie)?

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Homework Help Overview

The discussion revolves around finding the maxima and minima of the function f(x) = 2cos(3x) + 3sin(2x) on the interval (-π, π). Participants are exploring the process of differentiation and critical point analysis within this context.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to find the derivative of the function and question the correctness of their attempts. There is mention of using the chain rule and equating the derivative to zero to find critical points.

Discussion Status

Some participants have provided guidance on the differentiation process, while others are verifying the correctness of the derivative obtained. Multiple interpretations of the derivative and its implications for finding maxima and minima are being explored.

Contextual Notes

There is an emphasis on showing work and the requirement to adhere to homework rules, which may limit the information shared in the discussion.

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Homework Statement



find the maxima and minima of the function f(x)=2cos3x + 3sin2x on the interval (-pie, pie)

Homework Equations





The Attempt at a Solution

 
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You must show your work, before we can help you. What have you tried> Maybe something involving the derivative?
 
im not sure if i did the derivative right. i got -2sin3x+ 3cosx as the first derivative
 
ryan.1015 said:
im not sure if i did the derivative right. i got -2sin3x+ 3cosx as the first derivative

I'm sure that you didn't. You need to use the chain rule. Your answer should start with "f'(x) = "
 
pere callahan and mark44, is the following statement right..
find derivative of f(x) as below
f'(x) = -6sin(3x) + 6cos(2x)
now solve it by equating to zero. then find critical points. from these points and end points (pie and -pie) find the absolute maxima and minima & relative maxima and minima
 
ElectroPhysics said:
pere callahan and mark44, is the following statement right..
find derivative of f(x) as below
f'(x) = -6sin(3x) + 6cos(2x)
It is.
 

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