Optimization: find zeros of a derivative

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Homework Help Overview

The problem involves finding the maximum point of the function P(h) = -10h + 4410 - (6800/h), specifically by analyzing its derivative to locate critical points.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the derivative P'(h) = -10 + (6800/h^2) and explore how to isolate h from this equation. There is mention of multiple roots and the implications of considering h > 0. Questions arise about the correctness of derived values and the interpretation of the derivative.

Discussion Status

The discussion is ongoing, with participants clarifying their understanding of the derivative and its roots. Some guidance has been offered regarding the process of solving for h, but there is no explicit consensus on the correct interpretation of the results.

Contextual Notes

There is a mention of a specific answer (h = 82.5) provided by a teacher, which has led to confusion among participants regarding the calculations and assumptions made in the problem-solving process.

BeccaHua
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Homework Statement


Find the maximum point of P(h)=-10h+4410-(6800/h)


Homework Equations


P(h)=-10h+4410-(6800/h)

The Attempt at a Solution


P(h)=-10h+4410-(6800/h)
P'(h)=-10+(6800/h^2)
P'(0)=-10h^2+6800
10h^2=6800
Divide both sides by 10:
h^2=680
and sqrt both sides:
h=26.1
 
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BeccaHua said:

Homework Statement


Find the maximum point of P(h)=-10h+4410-(6800/h)


Homework Equations


P(h)=-10h+4410-(6800/h)

The Attempt at a Solution


P(h)=-10h+4410-(6800/h)
P'(h)=-10+(6800/h^2)
P'(0)=-10h^2+6800
10h^2=6800
Divide both sides by 10:
h^2=680
and sqrt both sides:
h=26.1

h=sqrt(680) isn't the only root, there's also h=(-sqrt(680)). Or are you only considering h>0? You'll still want to consider what happens near h=0. What's your question?
 
Oops sorry.. My question is how do you isolate h from P'(h)=-10+(6800/h^2)
I know the correct answer is h=82.5 but I'm not sure how to get there. I know that the sqrt of 6800 is 82.5 but then what happens with the -10?
 
BeccaHua said:
Oops sorry.. My question is how do you isolate h from P'(h)=-10+(6800/h^2)
I know the correct answer is h=82.5 but I'm not sure how to get there. I know that the sqrt of 6800 is 82.5 but then what happens with the -10?

If you are trying to solve 0=-10+(6800/h^2) to find a point where the derivative equals 0 then I think you already did it correctly. That means 10=6800/h^2 so 10h^2=6800, h^2=680. The derivative isn't 0 at h=82.5. That's wrong.
 
Okay thank you! The answer that was given was my teacher's answer and I was going crazy trying to figure out what I was doing wrong.
 

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