You are here:

Calculus/max- min optimization

Advertisement

Expert: - 2/1/2009


Question
An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x axis. The vertices of the base are on the curve 5y = 25 - x^2. find the area of the largest triangle.

Answer
The area of a triangle is known to be bh/2 where b is the base and
h is the height.  In this triangle, the height is y and the base is
twice the x coordinate, or 2x.  This would mean that bh/w
would be 2xy/2 = xy.

Now from the equation, we know that y = (25 - x²)/5, so the area
is x(25-x²)/5.  This can be rewritten as (25x-x^3)/5.  Taking the
derivative gives us (25 - 3x²)/5.  Set this to 0 and it gives
the equation 25 = 3x², or x²=25/3, or x²=3*25/9, so that the
squareroot can be taken easily, giving x=±5√3/3.  Note that if
x as taken as -5√3/3, the same triangle is generated as if x
were taken as 5√3/3, since they are just the same triangle reversed.

Taking the second derivative will make sure that this is a maximum.
The second derivatve is -2x/5.  This will be negative since we took
x as the positive value (since area is usually thought of as
a positive thing), which means that the point is a maximum.

Now if we took the negative value, it would be a minimum.
That is, the greatest negative area possible, but area is
usually not thought of being negative ... but it could be ...

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2012 About.com, a part of The New York Times Company. All rights reserved.