Question

If 600 cm2 of material is available to make a box with a square base and a closed top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.

Answer 1

(If the base has side x and the box has height h, the area

2x^2 + 4xh = 600,
h = (300-x^2)/2x

So, the volume

v = x^2 h = 150x - x^3/2

dv/dx = 150 - 3/2 x^2

So, dv/dx=0 when x^2 = 100

I think you can take it from there, ok?