Find the points on the curve y = 2 - # where the slope of the tangent is 14. Mark: 6 Find a quadratic function in the form y = ax + bx + c, which passes through the point (4,4) such that the slope of the tangent line at x=2 is -1, and the slope of the tangent line at x=8 is 11. Mark: 6In a real-life scenario, what would the marginal cost of producing an item represent? How does this relate to the equation modelling the cost of producing these items? Mark: 3 Explain the process you would use to nd when the slope of a tangent line of a given function is zero Mark: 3 How can you use the product and chain rule instead of using the quotient rule to differentiate a function? Mark: 3 How can you use ONLY the product rule instead of the chain rule to differentiate a function? Mark: 3 Alice the Amoeba is travelling according to the equation 5 = t3 ~6t2 +9t+ l , t is greater than or equal to 0, where sis displacement in metres and t is time in seconds. a What is her velocity after 3 seconds? b. Find her velocity when acceleration is Ont/$2 c. When is Alice at rest? d. When is Alice moving backwards? e. Draw a diagram of the rst 6 seconds. State the distance at each second on the graph. Mark: 6 In order to prove his strength to Marge, Homer throws a bowling ball upward such that its height h in metres aer a time t in seconds is given by the equation h = -4.9t2 + 19.6t. a. When does the ball land back on the ground? b. What is the velocity of the ball when it slams in to the ground? c. What is the acceleration of the ball when it is at its peak? Mark: 6 A hotel owner nds that an average of 150 rooms are booked when the price is $180 per night and 160 rooms are booked when the price is $160 per night. a Determine the price to maximize revenue b. Determine the maximum revenue