Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
Pages: 1
#1 2024-03-19 03:11:51
- nycguitarguy
- Member
- From: Brooklyn, NY
- Registered: 2024-02-24
- Posts: 566
Cross-sectional Area
The cross-sectional area of a beam cut from a log with radius 1 foot is given by the function A(x) = 4x•sqrt{1 - x^2}, where x represents the length , in feet, of half the base of the beam.
A. Which value of x maximizes the cross-sectional area?
B. What should be the length of the base of the beam to maximize the cross-sectional area?
The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.
Dr. David Jeremiah
Offline
#2 2024-03-19 06:29:11
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,210
Re: Cross-sectional Area
I've used the graph plotter to view what the graph of A against x looks like. I don't think you'll get the exact maximum without calculus but you can zoom in on the point using the plotter and get a value that way.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
Offline
#3 2024-03-19 10:37:49
- nycguitarguy
- Member
- From: Brooklyn, NY
- Registered: 2024-02-24
- Posts: 566
Re: Cross-sectional Area
I've used the graph plotter to view what the graph of A against x looks like. I don't think you'll get the exact maximum without calculus but you can zoom in on the point using the plotter and get a value that way.
Bob
Show me the Calculus way. I know a little bit of Calculus.
The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.
Dr. David Jeremiah
Offline
#4 2024-03-19 16:45:52
- KerimF
- Member
- From: Aleppo-Syria
- Registered: 2018-08-10
- Posts: 170
Re: Cross-sectional Area
The calculus way is based on the knowledge of the derivatives of functions.
Offline
#5 2024-03-19 20:27:32
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,210
Re: Cross-sectional Area
That will be zero when
Then solve that quadratic.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#6 2024-03-20 02:38:41
- nycguitarguy
- Member
- From: Brooklyn, NY
- Registered: 2024-02-24
- Posts: 566
Re: Cross-sectional Area
That will be zero when
Then solve that quadratic.
Bob
I see. You used the product rule. I am familiar with this rule.
The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.
Dr. David Jeremiah
Offline
#7 2024-03-20 02:39:53
- nycguitarguy
- Member
- From: Brooklyn, NY
- Registered: 2024-02-24
- Posts: 566
Re: Cross-sectional Area
The calculus way is based on the knowledge of the derivatives of functions.
I am familiar with basic differentiation. I just didn't know that the product rule can be used to solve this application.
The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.
Dr. David Jeremiah
Offline
Pages: 1