1. Consider the function /(x) = x"e-2* for x 2 0, where a is some unknown constant greater than 2. A. Find the constant a for which the function /(x) attains its maximum value at x = 3. Make certain to justify that a maximum is attained. B. For # = 4, find all x values of points of inflection for the curve y = (x). 2. Camille launches a model rocket in an open field near her house. The rocket has a bit of a problem, being slightly off balance. Its trajectory is described by the function y = 60 In(x + 1) - bix for 0 0, where , is in seconds. Find the time (r> 0) at which the velocity of the particle is 0, and find the particle's acceleration at that time as well. You must find exact values-don't approximate with a calculator. 4. Given In ( $ ) + 13 - 2x = -1. A. Find the equation of the normal line to the curve In ($ ) + 13 - 2x = - 1 at the point (1, 1).B. Find the equation of a tangent line to the curve y= e(*") that also passes through the point (1,0). You can approximate your final answer with your calculator after you've shown your work