Optimization: find zeros of a derivative

[BeccaHua]

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

 

[Dick]

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?

 

[BeccaHua]

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?

 

[Dick]

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.

 

[BeccaHua]

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.