A function f has a relative maximum at x = 2 and a point of inflection at x =-1. Find the critical points of . Describe what happens at each new critical point.
2. A 12.5 centimeter by 34 centimeter piece of cardboard will have eight congruent squares removed as in the diagram. The box will be folded to create a take-out hamburger box.
a. Find the model for the volume V(x) of the box as a function of the length x of the sides of the eight squares removed.
b. What are the dimensions of each of the eight squares that should be removed to produce a box with maximum volume?
c. Construct a physical model of the box and measure its volume. Compare this result to the result from the mathematical model