Finding Derivitive of a Triangle Area

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SUMMARY

The discussion focuses on finding the derivative of the area of a triangle given by the equation A = \frac{-4m^2 + 4m - 1}{m}. The user attempted to differentiate the area, resulting in \frac{dA}{dm} = \frac{4m^2 - 4m - 1}{m^2} and found m = 1/2. However, the textbook solution indicates that the correct values for m are +/- 1/2, highlighting a potential misunderstanding of the problem's requirements. The user questions the completeness of the problem statement, suggesting that additional context may be necessary for a full solution.

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My answer to this question seems close to that of the book but I have only solved for +1/2 and not the -1/2. Can anyone help?
Many thanks.

Homework Statement



Q. The area of a triangle is [itex]\frac{-4m^2 + 4m - 1}{m}[/itex]. Find the value of m via differentiation.

Homework Equations




The Attempt at a Solution



Attempt: [itex]\frac{dA}{dm}[/itex] = [itex]\frac{4m^2 - 4m - 1}{m^2}[/itex] = 0 => 4m2 - 4m + 1 = 0 => (2m - 1)(2m - 1) => m = 1/2

Ans.: (From textbook): [itex]\frac{dA}{dm}[/itex] = [itex]\frac{-4m^2 + 1}{m^2}[/itex] = 0 => m = +/- 1/2
 
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The question makes no sense and sounds incomplete. Find m by differentiation? That's not the derivative of A either. Are you sure you're not missing a portion of the problem?
 

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