Practice: Answer all questions by 7:30. I need to rewrite it then send it by 8:00. So please give by 7:30. Show all your work and make sure it is correct.

Question 1 (5 points) Derivatives a. Use limits to find the derivative of the following function: f(:L') [2 marks] b. Find the initial velocity_ of an object moving in a straight line if the displacement relation is given by: m=(y2)\/y|4 y>4 [3marks] Note: x represents time in seconds and y is displacement in meters. Question 2 (5 points) Curve Sketching Problem a) Using what you know about the curve sketching algorithm, show that 3 y = tan (em ) is a monotonic function (either never increasing or never decreasing). [4 marks] b) What point on the original curve is the slope zero? Exact answer only. [1 mark] Question 3 (5 points) Optimization Problem A chord parallel to the y-axis is inside of a loop described by the equation y2 = 332(24 51:). Calculate the maximum length of the chord. NOTE: Desmos or another graghing program cannot be used to obtain the answer. A full algebraic solution is required to obtain the maximum length. Mgr