6. Given the function and its first and second derivative function, 8 marks f(x) = X-2x-3 f'(x) = 2x+6 x2 x3 - and f" (x) =_ -4x-18 A. Determine the critical numbers of f(x) and determine the intervals where the function, f(x), is increasing and decreasing. A4 B. Determine the coordinates of the point(s) of inflection for /(x) and state the intervals of concavity. Your inflection point(s) must be (xy) form. A4PART 2: VECTORS [40 min] BEFORE THE SUMMATIVE: Draw using a marker the following given two vectors, 04 and OB Label these vectors on your model. DA = (0, -3, 4) OB = (6, -2,0) OC = (4,0,2) The coordinate of point A is B is and C is DRAW THE VECTOR OC =( _) on the day of the summative. [1K] For the following questions, refer to the ABOVE for information about points A, B and C. 1. Determine the magnitude of [AB| in exact values. [1K] 2. If OD = 20A - 08 + 1 0C, a) Determine OD . b) Is OD collinear to O4 ? Explain how you know. [3, K,A,T] 3. Draw and label on your model the vector XY , where point X is (0, 0, -4) and XY is collinear to OA Make sure you label the head and the tail as X and Y. [2 K, A] The coordinate of your Y point is :4. Calculate the angle in degrees between vectors 04 and OC . Round to one decimal place. [2 K, A, C] 5. a) A line, Li, crosses point A and another point X (1, -2, 5). Represent this line in vector equation form and parametric form. [ 3K] b) Calculate where the line Li intersects the xz- plane and xy-plane. Using what you know about Li, use the skewer and your model to represent Li. Label on your model the two punctured points. [3 K, A]6. FOR THE FOLLOWING PROBLEM, CREATE THE VECTOR DIAGRAM ONLY. A plane travels with an GROUND VELOCITY velocity of 325km/h at a direction of [S60W]. The wind is coming directly from the east at 40 km/h. Determine the air velocity and direction. [2 K,A]