1. The open-topped box is to be manufactured by cutting the square from each corner of 26-in. by 52-in. rectangular piece of cardboard and then folding up sides. What size squares must be cut from each corner to maximize volume of box and find maximum volume of box?
2. Determine all critical points of f(x)=2x4+16x3+36x2 and categorize each as the relative minimum, relative maximum, or neither one.
3. Determine average rate of change of h(x)=-2x4+15x3-3 between x = -4 and x= -2.
4. Determine equation of line tangent to g(x)=x2ln(2x-7) at x=4.