derivatives

Applications of derivatives

A rectangle has its base on the x axis and its upper two vertices on the parabola y=12 - x^2.
What is the largest area the rectangle can have, and what are its dimensions.
Support your answer graphically.
Thanks.

Well, the parabola is symettric about x=0, so just solve the half of rectangle, with x=0 being the one side, and x the other.

Area= xy= x(12-x^2)= 12x-x^3

dA/dx= 12 -3x^2 or setting to zero, x=2

Now applying symettry, the rectangle is from x=-2 to x=2

Area= INt ydx from x=-2 to 2
INT (12-x^2) dx= 12x-1/3 x^3 limits..
Area= 12*2 - 1/3 (-8) + 12*2 +1/3(8)
2(8-8/3)

I don't know what support graphically means, unless it means draw a graph.

check my work.

x = 4 and y = 8

the area = 32

  1. 👍 0
  2. 👎 0
  3. 👁 180
asked by Jen

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    A rectangle has its base on the x-axis and its 2 upper corners on the parabola y=12-x^2. What is the largest possible area of the rectangle?

    asked by pam on January 8, 2009
  2. calculus

    a rectangle has its base on the x-axis, and its upper corners in the graph of y=27-x^2. what is the maximal area of this rectangle?

    asked by michael on November 1, 2012
  3. calculus

    A rectangle has its base on the x-axis and its upper two vertices on the parabola y=12−x2 . What is the largest area that the rectangle can have

    asked by jim on May 19, 2009
  4. Math

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=9-x^2. What are the dimensions of such a rectangle with the greatest possible area?

    asked by Mary on November 4, 2008
  5. Calculus

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 6-x^2. What are the dimensions of such a rectangle with the greatest possible area?

    asked by Alessandra on November 4, 2014
  6. CALC

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=9–x2. What are the dimensions of such a rectangle with the greatest possible area?

    asked by Adam on May 29, 2010
  7. CALC

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=9–x2. What are the dimensions of such a rectangle with the greatest possible area?

    asked by Adam on May 30, 2010
  8. Calculus

    A rectangle is inscribed with its base on the x -axis and its upper corners on the parabola y= 11-x^2. What are the dimensions of such a rectangle with the greatest possible area?

    asked by Anonymous on October 27, 2011
  9. Calc Help Please

    A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola f(x)=8-x^2. What are the dimensions of such a rectangle with the greatest possible area?

    asked by Anonymous on August 8, 2013
  10. Calculus

    A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y= 12 - x^2. What are the dimensions of such a rectangle with the greatest possible area?

    asked by Marissa on June 1, 2011

More Similar Questions