Consider the following function:

f(x) = x1/2 " x3/2, x > 0

(a) Show that the function is strictly concave. Is the function strictly monotonic? Why or why not? Justify your answer.

(b) Find the global maximum x! and calculate the maximum value of the function, i.e., f(x!). If necessary, round your answers to two decimal places. Graph the function indicating all the critical points (intercepts and maximum point).

(c) Find the second order (n = 2) Taylor polynomial of the function f(x) at x = 1.

(d) Show that the second order Taylor polynomial is a strictly concave function and find its global maximum x!. In the same graph of part (b), graph the second order Taylor polynomial indicating all the critical points (intercepts and maximum point).