- Problem set 8, question 2 (range over which to graph a function)?
- Find list of x values for critical points, inflection points, covering each increasing/decreasing interval
- Want to graph from slightly less than smallest value in list to slightly more than largest in order to see all “interesting” features of function
- Do manufacturers of buckets actually use dimensions that
come close to minimizing the amount of material needed to
make the bucket?
- Bucket = cylinder
- Surface area proportional to amount of plastic and cost
- = 2πrh + πr2
- Volume V = πr2h gives
- h = V/(πr2)
- h = V/(πr2)
- Optimal r = (V/π)1/3
- For 2.5 gallons...
> V = 2.5 * 231 > V [1] 577.5 > (V/pi)^(1/3) [1] 5.685919 > r = (V/pi)^(1/3) > h = V/(pi*r^2) > h [1] 5.685919- Optimal r = 5 2/3 inches, h = 5 2/3 inches
- Actual r = 4.25, h = 9.5
- One more quick optimization example
- Introduction to integration
- Read section 5.1