Optimisation and word problems
Differentiation · Mathematics
Study notes
Q: A rectangular box with square base, no top, volume 32 m^3. Minimize surface area. Let base side x, height h. x^2·h = 32, so h = 32/x^2. S = x^2 + 4xh = x^2 + 128/x. S' = 2x - 128/x^2 = 0: x^3 = 64, x = 4. h = 2. S'' = 2 + 256/x^3 > 0: minimum. Min S = 16 + 32 = 48 m^2.