(1) (a) (12 points) Find all numbers c in the interval (3, 4) so that the tangent line to the graph of f(x) = 3+VI-3 at c = e is parallel to the line through (3. (3)) and (4, f(4))- (b) (13 points) If f"(x) = 31\\+ + sinx + 82x, f(0) =0, and f'(0) =0, find f(x). (2) (a) (12 points) After 3 days, a sample of a radioactive substance decayed to 58% of its original amount. Find the half-life of the substance. Do not evaluate your answer. (b) (13 points) Find the extreme values of the function f( )= 3+ 12 (3) (a) (13 points) Find the area of the largest rectangle that can be inscribed in a right triangle with legs of length 3 and 4 if two sides of the rectangle lic along the legs. (b) (12 points) Find the limit. lim Ar + 1