Analytical. Required to be written by hand.

Consider the function f : D - R given by f(x) = vx-x. With the aid of graphs, answer the following. (a) Find the derivative of f. Is the function strictly increasing, decreasing or neither? (b) Find the second derivative of f. Is the function strictly concave, strictly convex, or neither? (c) Suppose D = [0, 1] find the maximum and the minimum of f. (d) Suppose the domain D = (0, 1), find the maximum and the minimum of f. (e) Suppose the domain D = [0, co), find the maximum and the minimum of f. (f) What conditions on D are necessary to guarantee both a maximum and a minimum