(4) (a) Using the definition of the derivative, find the derivative of f(r) = r+; (b) State the domain of f and f'. (5) Sketch the graph of a function that satisfies all of the given conditions. . f'(x) > 0, for all x # 1 . r = 1 is a vertical asymptote . f" > 0, for r E (-00, 1) U(3, co) . r = 3 is an inflection point. (6) Prove that the equation r' + r - 1 = 0 has exactly one real root. (Hint: Rolle's Theorem). (7) Find the derivative of the function: y = V1 + todt. sin F