differentiation help

• lavastar

  9 Sep 07, 21:31

  A container, in the shape of a right pyramid with a square base, has a given surface area A. If the side of the base is of length x, prove that the volume V is given by 36V^2=(Ax)^2 -2Ax^4. Find the value of x for which V is maximum, and show that max value of V is (A^3/2) divide by sq root 288.
  
  I have problem for proving the 1st part.. any help please? thanks
• oOprinceOo

  9 Sep 07, 21:32

  so chim i dont understand. wait for the pro to come
• ispyyy

  9 Sep 07, 21:59

  solution is as below :
  
  http://mathworld.wolfram.com/SquarePyramid.html
  
  
• eagle

  9 Sep 07, 22:17

  if u know what a right pyramid is, you can easily do the brute force method
  
  Find V in terms of x = 1/3 * 1/sqrt(2) * x^3
  Find A in terms of x = (sqrt(3) + 1) x^2
  
  Sub into equation and done
  
  You can then easily differentiate to find x where V is max
  and then sub x into equation and u get the final answer