Contextual Applications of Differentiation Discussion-Based Assessment Assigned Problems e" 1 Sll'l X function such that gm] = G. The graph of g'. the derivative of g, is shown. 1. Let f be the function dened by fix) = . Let g be a differentiable Part A: Find the value of Ligor state that it does not exist. Justify 1your answer. Part 5' Find the value of lint x} or state that it does not exist Justify:r your ' Hem ' answer. 2. The edges of an ioe cube are expanding at a constant rate of 1 inch per minute. Part A: At the time when the edge of the cube is 6 inches. what is the rate of increase of its volume? Part B: How fast is the surface area of the cube changing when each edge of the cube is 3 inches? Part C: A second ice cube is changing such that :7\": 25. Interpret the meaning of this value and describe how the second ice cube is changing. 3. A cylindrical container lled with snow cone syrup has a diameter of 4 inches and a height of 1G inches. The container is full of syrup and leaking at a rate of 2 inaihr. The syrup is leaking into an empty conical snow cone cup with a diameter of 2.5 inches and a height of 3.5 inches. Part A: How fast is the depth of the syrup in the cylinder changing when the level in the cylindrical container is 3 inches high? Part B: At what time will the cylindrical syrup container be empty? Part C: At what rate is the depth of the syan in the conical cup rising when the syan in the cup is 1 inch deep? Indicate units of measure. 4. A parlicle moves along the xattis so that its position. in feet. at time t seconds is given byyrjtju= 4? + EH 2 e'fortime III 5 t55. Part A: What is the velocity of the particle when the acceleration is zero? Part B: When is the particle moving to the right? Justify your answer. Part C: At time t = 2. is the particle speeding up or slowing down? Give a reason for your answer. 5. Let f be a differentiable function. Selected values of f and its derivative f' are given in the table in the closed interval -2 s x 2, where f' is strictly increasing on the interval (0, 2). X -2 -1 2 f(x) 20 17 11 7 1 f' (x) -10 -8 -4 -2 -1 Part A: Find the linearization f(x) at the point where x = 1. Part B: Use the line from part A to approximate the value of f(1.3). Is this approximation greater than or less than the actual value of f(1.3)? Give a reason for your