Written Exercises (13 points total) Exercise 1. (Component Skill 6.1) A tornado passes over a weather station with a barometer that was recording atmospheric pressure as a function of time1 . Several weeks after the storm passed and clean-up efforts concluded, meteorologists at the weather station fit the pressure data to a curve and found the following relationship: p(t) = 1 12t 57 + 16(t 2) 2 . Here, t is time in minutes after the tornado sirens first went off, and p(t) is the atmospheric pressure (measured in standard atmospheres) at the weather station. The tornado destroyed the barometer after t = 3 minutes, so the relationship above is valid only for 0 t 3. a. Is p(t) a unimodal function over 0 t 3? Justify your answer by finding the critical point(s) of p(t) over the interval 0 t 3. Hint: Please use Wolfram Alpha to calculate p (t). b. Show that your critical point from (b) is a local minimum using the second derivative test. Hint: Please use Wolfram Alpha to calculate p (t). c. What is the minimum pressure recorded at the weather station over 0 t