Answers in exact form plzAnd explaination

(4 marks) 4. Determine the equation of the tangent line to the curve 32x - 23 = Ary at the point (1, 1). (4 marks) 5. To cars start moving from the same point at noon. One travels north at 40 km/hr, and the 2pm? other travels west at 75 km/hr. At what rate is the distance between the cars increasing at 6. Let f(x) = x(2 -4)3. (1 mark) (a) Find the domain of f(x). (1 mark) (1 mark) (b) Find the coordinates of the r- and y-intercepts or explain why they do not exist. (2 marks (c) Determine the equations of any horizontal or vertical asymptotes of f(x), if they exist. (d) Show that f'(x) = 4(x - 4)2(x - 1) and f"(x) = 4(x - 4)(3x - 6). (2 marks) (e) Find any critical points of f(x) and determine the intervals of increase and decrease. (2 marks (f) Determine the intervals of concavity and locate any points of inflection of f(I). (3 marks) (g) Sketch the graph of y = f(x) using the above information. Label all important points, including local extrema, inflection points, intercepts, and asymptotes. (4 marks) 7. Use linear approximation to approximate the value of V66 to 3 decimal places. Hint: Let f(x) = Vx, and a = 64. 8. Evaluate the following integrals. Show all of your work. (3 marks) (a) (3 marks) ( b) ( e"VItexdoc 9. A company's marginal revenue is given by R'(x) = -612 +70x + 180 and the marginal cost is given by C'(x) = 20x + 80 where a is the number of items produced. WIN (a) What is the production level that will maximize profit? (2 marks) (b) What is the maximized profit?