A manufacturer designs a cylindrical can to hold a fixed volume of liquid
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A manufacturer designs a cylindrical can to hold a fixed volume of liquid. After finding the critical point of the surface-area function expressed in terms of the radius, the manufacturer also computes the second derivative. Which of the following best explains why this additional computation is necessary?
(a) To determine the exact location of the critical point by solving S′′(r)=0.
(b) To confirm that the critical point satisfies the fixed volume constraint.
(c) To verify that the critical point corresponds to a minimum amount of material rather than a maximum.
(d) To adjust units so that the derivatives of surface area have the same units as the surface area itself.