Solving Derivative Question: How to Explain Why it's Negative?

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Homework Help Overview

The discussion revolves around a derivative question, specifically addressing the reasoning behind a negative result in a calculus problem. Participants are exploring the implications of their calculations and the relationships between different mathematical expressions.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the substitution method used in the original attempt and question how to articulate the negativity of the derivative. Suggestions include comparing different mathematical expressions and exploring specific values to simplify the analysis.

Discussion Status

The conversation is ongoing, with participants sharing hints and suggestions without reaching a consensus. Some guidance has been offered regarding comparisons and specific values to consider, but no clear resolution has emerged yet.

Contextual Notes

There is an indication of a need for further exploration of the relationships between functions involved in the problem, as well as the potential impact of chosen parameters on the outcome.

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Homework Statement


[PLAIN]http://img696.imageshack.us/img696/4462/124234c23c423.jpg


The Attempt at a Solution



I did the first part already, by letting
u = ax => dx = du/a, then just substituting in the values.

How do i explain why its negative?
 
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Try comparing the value of [itex]e^{-x}[/itex] to the value of [itex](1+x)^{-1}[/itex]. Then prove the relationship you find, maybe with series expansions or some other way.
 
Hint: Its value doesn't depend on α. Find a nice value of α. to try.
 
Im still stuck :(
 
What nice value of α have you tried?
 

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