Solving Calculus Doubts: My Attempt

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    Calculus Doubts
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SUMMARY

The discussion focuses on solving a calculus problem where the variable ##k## may be negative, affecting the direction of the inequality. The user suggests two effective methods to address this issue: performing three separate cases for ##k## (positive, negative, and zero) or multiplying by ##|k|## to maintain the inequality's validity. The second method is noted as quicker but requires careful validation steps. This approach ensures accurate conclusions in calculus problems involving inequalities.

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Portuga
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The problem, and my attempt to solve it is here:
https://meocloud.pt/link/bf620660-aaf0-48ad-abfe-ac49f7ea0843/calculus_doubt.pdf/
 
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It's almost right. The only problem is that ##k## may be negative. So multiplying the inequality by ##k## will change direction of the inequality, which will prevent reaching the conclusion.

Two ways to get around this are:

1. Do three separate cases, for k positive, negative and zero respectively; or
2. Multiply by ##|k|## instead.

2 is quicker, but you'll need to insert a few careful steps around where you multiply by ##|k|## to ensure that each one is valid.
 
Thank you very much!
 

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