1. (4 pts) Consider the function f(x) = 2 2 + 3 (a) Give the domain of the function and list any intercepts and asymptotes. (b) Give the intervals for which f is increasing or decreasing. Classify all extrema.() Give the intervals for which f is concave up or concave down. Identify all inflection points. (d) Give a rough sketch of the graph of f(z). 2. (3 pts) A rectangle is bounded by the z-axis and the semicircle y = /64 22 (a) Draw a picture modeling the situation. (b) Suppose the rectangle meets the semicircle at the point (a, b) in the first quadrant. Find a formula for the area of the rectangle in terms of a and find its derivative. () What choice of a yields the largest area? What is this maximum area? 3. (3 pts) The sum of the perimeters of an equilateral triangle and a rectangle whose length is twice its width is 60. (a) Let x denote the width of the rectangle. Draw a picture modeling the situation and label all the sides of the shapes in terms of x. (b) Find a formula for the total area enclosed by the two shapes in terms of = and find its derivative. () What dimensions of the triangle and rectangle produce a minimum total area? What is this minimum area