How to find increasing and decreasing intervals of a biquadratic function?

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Homework Help Overview

The discussion revolves around determining the increasing and decreasing intervals of the biquadratic function y = -x^4 + 18x^2 + 11. Participants explore the process of finding critical points through the first derivative.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster suggests finding the first derivative and critical points as a method. Some participants agree, mentioning the use of a sign chart for the first derivative to gather necessary information.

Discussion Status

The conversation is active, with participants confirming the approach of using the first derivative and discussing the implications of the biquadratic nature of the function. There is acknowledgment of a local minimum at one of the critical points.

Contextual Notes

Participants note that the first derivative leads to a third-order equation, which may simplify the process of finding critical points. There is an implicit understanding of the function's characteristics based on its biquadratic form.

courtrigrad
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Hello all

Given [tex]y = -x^4 + 18x^2 + 11[/tex] how would you find the intervals where the function is increasing and decreasing? Would you have to find [tex]f'(x)[/tex] and find critical points?

Thanks
 
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Yep, that's the most straightforward and surefire way to do it.
 
yes that is the way to go...

make a sign chart of the first derivative and you'll have all the info you need

marlon
 
Due to the biquadratic character of the function,the resulting 3-rd order equation (when setting the first derivative to zero) can be solved easily.
One of the solutions is zero and is a local minimum.

Daniel.
 

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