Setting Derivative = 0 and solving

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SUMMARY

The discussion focuses on the legality of setting a derivative equal to zero and manipulating the equation to solve for the variable x. Specifically, the example provided involves the derivative expressed as (x-3) / (2x). Participants confirm that it is valid to multiply both sides by the denominator (2x) when setting the derivative to zero, leading to the simplified equation x-3=0, which results in x=3. Alternative methods, such as dividing by (x/x) when x is not zero, are also discussed as valid approaches.

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Homework Statement


I'm currently working on a problem that requires me to set the derivative = 0 and solve for a variable (call it x). The derivative comes out to be a fraction, with x terms in both the numerator and denominator. Is it legal to just multiply 0 by the denominator (thereby canceling it) even if it has the term of interest as part of it?

Simple Ex: say the derivative came out to be x-3 / 2x. And I want to solve for x.
When I set that derivative equal to zero, can i just multiply 0 by 2x, leaving x-3=0? So x=3

Homework Equations



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The Attempt at a Solution


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That should be ok. You could also divide the left side by x / x, assuming that x is not equal to zero, resulting in:

( 1 - (3/x) ) / 2 = 0
 
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thank you
 
rcgldr said:
That should be ok. You could also divide the left side by x / x, assuming that x is not equal to zero, resulting in:

( 1 - (3/x) ) / 2 = 0

i thought they're supposed to show the work?
 
MGCLO said:
i thought they're supposed to show the work?

It is a requirement for HW problems, but my question was geared towards a concept. The equation I'm deriving for the HW would probably take up an entire line on here. The example I put on was just that, an example, it wasn't even close to my actual problem (although I wish it was haha)
 
MGCLO said:
i thought they're supposed to show the work?
Multiplying both sides by 2x is just as valid as dividing the left side by x/x. I only showed that as an alternative in case there's a situation where that would be a better option for a different equation.
 

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