Question 2 (a) For the given graph of the function f, on the left, sketch the graph of of f' on the right. A A (b) For the given graph of the function f, on the left, sketch the graph of of f' on the right. A A 4 4 Question 4 Ultrasound is often used to make images of developing fetuses. In particular, by measuring the size of a fetus ultrasound technicians can estimate its age and then predict its birthdate. To do this requires formulas for fetus size as a function of age. Verbung et al. (2008) fit data from over 6000 fetal ultrasounds. They measured the femur length, L, (in mm) as a function of the fetus age, t, (in weeks) and found the following formula: L : 37.50 + 3.71t 6.33 x 104:3. (a) Calculate the rate of growth, dL/dt, at t :15, 20, and 30 weeks. Does the rate of growth of the fetus increase or decrease as it ages? (b) Write a sentence interpreting L'(15) in terms of the femur length, including units. Question 5 The revenue per month earned by the Couture clothing chain at time t is RU) : M030), Where N (t) is the number of stores and 305) is the average revenue per store per month. Couture releases a statement to their investors saying that currently they have 50 stores with a total revenue of $7,500,000 and expect to increase the number of stores by about 2 stores per month and increase total revenue by about $250,000 per month. What does this statement imply about the current rate of change of the average revenue per store per month? Question 6 Suppose that f is a function given by lm+5l ifmSl ue): mu\"? if 132. (a) At which mvalues does f not have a limit? (1)) At which wvalues is f not continuous? (C) At which mvalues is f not differentiable? Question 7 For the given graph of the function f, on the left, sketch the graph of of f' on the right. A Question 8 In 1999, the population of Richmond-Petersburg, Virginia1 metropolitan area, was 961,400 and was increasing at a at roughly 9200 people per year. The average annual income in the area was $30,593 per capita, and this average was increasing at about $1400 per year. Use the product rule to estimate the rate at which total personal income was rising in the area at this time. Explain the meaning of each term in the product rule