1. Differentiate the following. a) f (x) = (x -3)(x3 -2) b ) f (x ) = x3 - 2x+ 1 c) f (x) = (3x2 +x - 3)3 d) f ( x ) = 2x-1 x+2 e) f(x) = V2x - 12. The following graph illustrates distance vs time of a moving object. Use the graph to answer the following questions. [4 marks] Position Time a) In what interva|(s) is the object moving towards the origin? b) In what interval(s) is the objects' velocity positive? c) When does the object change direction? 3. The line 8x y 8 = O is tangent to the graph of f(x) = (x + k)(x2 1) at the point (1, 0). Find the value of k. 4. A company sells an average of 50 skateboards pe month at a price of $120 each. For each $5 decrease in price, two more skateboards are sold. Determine the marginal revenue when 25 skateboards are sold. I prefer explanations and answers written on paper. Please explain each question in detail for an accurate understanding. I prefer explanations and answers written on paper. Please explain each question in detail for an accurate understanding