1. Curve Sketching: Plot the rational function y = x^2+4 / 2x . (a) Identify the domain and range (b) find the critical points; (c) find where the curve is increasing and where it is decreasing; (d) find the points of inflection, if any occur, and determine the concavity of the curve; (e) identify any asymptotes that may exist; (f) plot key points and sketch the curve together with any asymptotes that exist.

2. Volume of a solid: The base of the solid is the region bounded by the parabola y^2 = 4x and the line x = 1 in the xy-plane. Each crosssection perpendicular to the x-axis is an equilateral triangle with one edge in the plane. (The triangles all lie on the same side of the plane.) Find the volume of the solid.