Calculus AB Assignment Analysis of Curves 1. Consider the function /(x) = x"e-2X for x 2 0, where n is some unknown constant greater than 2. A. Find the constant , for which the function /(x) attains its maximum value at x = 3. Make certain to justify that a maximum is attained. B. For n = 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 = 60In(x + 1) - 6x for 0 0, where : is in seconds. Find the time ( > 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 ( * ) + y3 - 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