Setting the derivative 0 and solving did I get the right results?

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Homework Help Overview

The discussion revolves around finding critical points of a function by setting its derivative to zero. Participants are examining the correctness of their calculations and interpretations related to the derivative.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the process of setting the derivative equal to zero to find critical points and question the validity of specific values obtained. There is an exploration of whether multiple solutions exist and the implications of undefined derivatives.

Discussion Status

The conversation is active, with participants providing feedback on calculations and questioning the completeness of the solutions. Some guidance has been offered regarding specific values of the derivative, and the discussion reflects a mix of confirmations and inquiries about the results.

Contextual Notes

There is mention of a point where the derivative is not defined, which may affect the analysis of critical points. Additionally, the original poster's attachment is referenced but not detailed in the discussion.

Femme_physics
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The function and my attempt to find the critical points by setting the derivative equal to zero are in the attachment. Is this correct?
 

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You have f'(x)=2x-16x-2.

Could you try calculating f'(2) and more specifically f'(8)?
If your solution is correct they should both be zero.
 
*smacks forehead*

Good idea! So 8 is definitely wrong, 2 is correct. Is 2 the only correct answer then?
 
Femme_physics said:
*smacks forehead*

Good idea! So 8 is definitely wrong, 2 is correct. Is 2 the only correct answer then?

Yes.

In general x3=a has 1 real solution (and 2 imaginary ones).
The real solution is x=a1/3.
 
I'll remember that. :) Much appreciated Serena...you're the best.
 
Also, don't forget about x = 0, where the derivative is not defined.
 

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