top 4 x
bottom 4 x
corners vertical 4 h
8 x + 4 h = 36
h = (36 - 8 x)/4 = 9 - 2 x (part i.)
v = x^2 h = x^2 (9 - 2 x) = 9 x^2 - 2 x^3
dv/dx = 0 for max or min
dv/dx = 18 x- 6 x^2 = 0
6 x ( 3 - x) = 0
x = 0 is minimum of course
x = 3 is maximum then
Problem solving with derivatives.
A rectangular box has square base of edge length x cm. Its framework of 12 edges is constructed from wire of total length 36cm. Find:
i. the height of the box in terms of x ?
ii. the volume of the box in terms of x?
ii. the value for x which the volume is a maximum.
1 answer
1 answer