# Optimization: find zeros of a derivative

1. May 8, 2013

### BeccaHua

1. The problem statement, all variables and given/known data
Find the maximum point of P(h)=-10h+4410-(6800/h)

2. Relevant equations
P(h)=-10h+4410-(6800/h)

3. 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

2. May 8, 2013

### Dick

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?

3. May 8, 2013

### 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?

4. May 8, 2013

### Dick

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.

5. May 8, 2013

### 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.