Max/Min Calculus Homework: Find Resistance for Max Power

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Homework Help Overview

The problem involves finding the resistance value that maximizes electric power, given by the equation p = 144r/(r + 0.8)^2, where r represents resistance in ohms. Participants are exploring the calculus concepts related to maxima and minima.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of the quotient rule to find the derivative and set it to zero to locate critical points. There are questions about the correctness of the derivative and the implications of the results obtained. Some participants suggest checking values around the critical point to confirm whether it is a maximum.

Discussion Status

The discussion is active, with participants confirming each other's calculations and suggesting methods to verify the maximum point. There is an emphasis on using derivative tests and plotting the function to explore the behavior of the power function around the critical point.

Contextual Notes

Participants are navigating assumptions about the nature of the maximum and the implications of having a single critical point. There is a mention of using computer algebra systems for verification, indicating a reliance on technology for further exploration.

uradnky
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Homework Statement


The electric power in Watts produced is given by p= 144r/(r+.8)^2
where r is the resistance in ohms.
For what value of r is the power P a maximum?

Homework Equations





The Attempt at a Solution


Using the quotient rule i found a derivative of..

dp/dt= 144(-r+.8) / (r + .8)^3

Now I need to set this equal to zero and solve for R?

Multiplying the demonminator by 0 would leave me with just the numerator giving me..
-144r + 115.2 = 0

Solving for r gives me r = 0.8ohms


Was there maybe a problem with my derivative?
 
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You did it right, find where the derivative is equal to 0 ... [tex]144(.8-r)=0[/tex]

Solve for r which you did! Is that not the correct answer?
 
Last edited:
Looks right to me. You can always check to see if you've found a local maximum using the first or second derivative tests and plugging it back into the original function.
 
Test values before and after your max-value: positive to negative should indicate a max-point.
 
Thanks for confirming it for me. Plugging .8 into the derivative gives me 0 so i guess i was right all along.
 
Actually, you'd want to plug in something less than 0.8 and more than 0.8 in the derivative to see if it changes from positive to negative in order for 0.8 to be a maximum.
 
Plot the power function for vallues of r from 0 to 10 using a
computer algebra system like Mathematica and you will verify that
the answer 0.8 for the maximum value looks correct.
 
jimvoit said:
Plot the power function for vallues of r from 0 to 10 using a
computer algebra system like Mathematica and you will verify that
the answer 0.8 for the maximum value looks correct.
You don't need to do all that! Just do what Snazzy or I suggested. Make good use of your Algebra skills!
 
Snazzy said:
Actually, you'd want to plug in something less than 0.8 and more than 0.8 in the derivative to see if it changes from positive to negative in order for 0.8 to be a maximum.

Yeah, with 1st derivative test right?
I just figured that it would be ok to assume a maximum because that's what the question asked for, and solving for r only gave me one value.
 

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