Sunday

April 20, 2014

April 20, 2014

Posted by **Isaac** on Monday, November 28, 2011 at 12:22pm.

A rectangle is to be inscribed with its base on the x-axis and its other two vertices above the x-axis on the parabola y=9-x^2

(a) find the dimensions of the rectangle of largest area.

(b) Find the area of the largest rectangle.

- Calculus -
**Steve**, Monday, November 28, 2011 at 1:18pmSince the parabola is symmetric about the line x=0, let the rectangle have corners

(-x,0) (x,0) (x,y) (-x,y)

Since y is 9-x^2, the rectangle is

2x by (9-x^2) in width and height. The area is thus

A = 2x(9-x^2) = 18x - 2x^3

To find the value of x which gives maximum area, we want

A' = 0

A' = 18 - 6x^2

A' = 0 when x = √3

So, the rectangle is

2√3 by 6 with area 12√3

**Related Questions**

Maths - hello Can someone please help me with solving simultanaous equations ...

Math - Hello I am having trouble with a pre-calculus problem. The problem is ln|...

calculus - hello here, Please can i get direction on website to practice ...

Algebra 1 - Hello! :-) Can some please explain to me or provide a website that ...

Calculus Please Help - Hello I'm reposting this question because right now it's ...

pre calculus - Hi, I am having a problem trying to find and understanding how ...

pre calculus - Hi, I am having a problem trying to find and understanding how ...

Pre Calculus Repost Please Help - Can someone help me solve this problem: cos^2x...

spell - What would be a good title for this essay? There is an underlying ...

Science - Hello. Can someone please show me a link or something to the Big Bang ...