1. Let f be a twice-differentiable function with derivative given by f (x) = 4x³ + 12x². Part A: Find the x-coordinate of any possible critical points of f. Show your work. Part B: Find the x-coordinate of any possible inflection points of f. Show your work. Part C: Use the Second Derivative Test to determine any relative extrema and inflection points. Justify your answers. Part D: If f has only one critical point on the interval [2, 4], what is true about the function f on the interval [2, 4]? Justify your answers.
2. The continuous function g, consisting of two line segments and a parabola, is defined on the closed interval [3, 6], is shown. Let f be a function such thatf(1)=e1 andf(x)=ex(x1). Part A: Complete the table with positive, negative, or 0 to describe g and g. Justify your answers. (3 points)

x	3 < x < 0	0 < x < 1	1 < x < 4	4 < x < 6
g(x)	positive	positive	positive	positive
g(x)
g(x)

Part B: Find the x-coordinate of each critical point of f and classify each as a relative minimum, a relative maximum, or neither. Justify your answers. Part C: Find all values of x at which the graph of f has a point of inflection. Justify your answers. Part D: Let h be the function defined by h(x) = 2f(x)g(x). Is h increasing or decreasing at x = 1? Justify your answer.