+270 A rectangluar open topped aquarium is to have a square base and volume 8m^3. The material for the base cost $1 per m^2, and the material for the sides cost $4 per m^2. What demensions minimize the cost of the aquarium??
+95 Have you done the one where it is asking to find the max area of a right triangle?
+95 V=x^2y = 8 => 8/x^2
C= 1*x^2+4(4xy)
C= x^2+16xy
C(x)= x^2+16x* 8/x^2
C(x)= x^2+128/x
C'(x)= 2x-128/x = 0
2x = 128/x^2
2x^3=128
x^3=64
x=4
C''(x)= 2+256/x^3 >0, for all x>0
By the second derivative test for absolute min, cost is minimum when x=4, y= 1/2
+95 Have you done the one where it is asking to find the max area of a right triangle?
