ASSIGNMENT #A 2008 BCS No Calculator (AB use a Calculator) 5. The derivative of a function f is given by S'(x) = (x - 3)et for & > 0, and / (1) = 7. (a) The function f has a critical point at x = 3. At this point, does f have a relative minimum, a relative maximum, or neither? Justify your answer. (b) On what intervals, if any, is the graph of f both decreasing and concave up? Explain your reasoning (c) Find the value of f(3). 2007 BC 4 No Calculator (AB skip part C) 4. Let f be the function defined for x > 0. with f(e) = 2 and f', the first derivative of f, given by f'( x ) = x2 In.x. (a) Write an equation for the line tangent to the graph of f at the point (e, 2). (b) Is the graph of f concave up or concave down on the interval I 4 ? Why?2003 AB 6 No Calculator 6. Let f be the function satisfying f'(x) = x f(x) for all real numbers x, where f (3) = 25. (a) Find f"(3). (b) Write an expression for y = f (x) by solving the differential equation dy dx = xvy with the initial condition f(3) = 25. 2008 AB 6 No Calculator 6. Let f be the function given by f(x) = for all x > 0. The derivative of f is given by f'(x) = 1- Inx X 2 (a) Write an equation for the line tangent to the graph of f at x = e-. (b) Find the x-coordinate of the critical point of f. Determine whether this point is a relative minimum, a relative maximum, or neither for the function f. Justify your answer. (c) The graph of the function f has exactly one point of inflection. Find the x-coordinate of this point. (d) Find lim f(x)