Maximum and Minimum Problems

Use the constraint to express the quantity to optimise in one variable. State the feasible domain. V (x)=0 Find the interior stationary points and test their nature. Compare admissible endpoints and relevant limits for a global maximum or minimum. Discard infeasible values. An excluded endpoint may give a limiting value that is never attained. Mensuration formulae **Solid** | **Volume** | **Curved surface area** Cylinder | pi r2h | 2pi rh Cone | 13pi r2h | pi rl Sphere | 43pi r3 | 4pi r2 Substitute back to find the requested quantity and include units. Add bases when total surface area is required.