3. Consider the real-valued function f(1) = 21r1r2 + 32571. (a) Establish the domain for f. (b) Identify any critical points. (c) Identify any inection points and nd intervals where the graph is concave up and concave down. (d) Use your results in parts (b) and (c) to establish the location of any local extrema (Second Derivative Test). 4. Consider the real-valued function f (2:) = 4x3 14.7:2 + 123:. (a) Establish the domain for f. (b) Identify any critical points. (0) Identify any inection points and nd intervals where the graph is concave up and concave down. (d) Use your results in parts (b) and (c) to establish the location of any local extrema (Second Derivative Test). 5. Squares with sides of length a: are cut out of each corner of a rectangular piece of cardboard measuring 3 ft by 4 ft as shown in the gure on the right. The resulting piece of cardboard is then folded into a box without a lid. (a) Write expressions (in terms of CL') for the length and width of the base of the box, as well as the height of the box. (b) Write an equation for the volume of the resulting box as a function of :r, and determine a reasonable domain (What values of a: will allow you to produce a box as described). (0) Using calculus methods, nd the volume of the largest box that can be formed in this way. Hint: compare with your work in problem 3 3 feet