Using derivatives to determine the increase and decrease of functions

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Homework Help Overview

The discussion revolves around using derivatives to analyze the increase and decrease of functions, focusing on the application of first derivatives in determining monotonicity.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the importance of finding the derivative of the function and identifying critical points where the derivative is zero or changes sign. There are inquiries about the meaning and calculation of the derivative, as well as attempts to clarify the steps involved in the analysis.

Discussion Status

Some participants have provided guidance on the steps to take, including finding the derivative and analyzing its sign. However, there appears to be a lack of consensus on the specific attempts made, as multiple participants mention various efforts without detailing them.

Contextual Notes

There is a mention of needing to see specific attempts to better understand where participants may be getting stuck, indicating that some information may be missing from the discussion.

samuelfarley
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Homework Statement
Given the function, f (x) = 4x^6 - 3x^5

show, using interval notation, where the function is decreasing and increasing.

Please give step-by-step details on using derivatives to analyze functions.
Relevant Equations
f (x) = 4x^6 - 3x^5
many attemps made
 
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What's ##f'(x)##?
 
samuelfarley said:
many attemps made
But to see where you are going wrong or getting stuck we need to see at least one of them.
 
First step is to find the derivative of the function ##f'(x)##. Then to find for which x is ##f'(x)=0##, for which x is ##f'(x)>0## and for which x is ##f'(x)<0##. Then using the monotonicity theorems that relate the monotony of a function to where the first derivative is positive or negative , you can find for which x the function is increasing and for which x the function is decreasing.
 

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